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T-structure

In the branch of mathematics called homological algebra, a t-structure is a way to axiomatize the properties of an abelian subcategory of a derived category. A t-structure on $$\mathcal{D}$$ consists of two subcategories $$(\mathcal{D}^{\le 0}, \mathcal{D}^{\ge 0})$$ of a triangulated category or stable infinity category which abstract the idea of complexes whose cohomology vanishes in positive, respectively negative, degrees. There can be many distinct t-structures on the same category, and the interplay between these structures has implications for algebra and geometry. The notion of a t-structure arose in the work of Beilinson, Bernstein, Deligne, and Gabber on perverse sheaves.

Definition
Fix a triangulated category $$\mathcal{D}$$ with translation functor $$[1]$$. A t-structure on $$\mathcal{D}$$ is a pair $$(\mathcal{D}^{\le 0}, \mathcal{D}^{\ge 0})$$ of full subcategories, each of which is stable under isomorphism, which satisfy the following three axioms. It can be shown that the subcategories $$\mathcal{D}^{\le 0}$$ and $$\mathcal{D}^{\ge 0}$$ are closed under extensions in $$\mathcal{D}$$. In particular, they are stable under finite direct sums.
 * 1) If X is an object of $$\mathcal{D}^{\le 0}$$ and Y is an object of $$\mathcal{D}^{\ge 0}$$, then $$\operatorname{Hom}_{\mathcal{D}}(X, Y[-1]) = 0.$$
 * 2) If X is an object of $$\mathcal{D}^{\le 0}$$, then X[1] is also an object of $$\mathcal{D}^{\le 0}$$.  Similarly, if Y is an object of $$\mathcal{D}^{\ge 0}$$, then Y[-1] is also an object of $$\mathcal{D}^{\ge 0}$$.
 * 3) If A is an object of $$\mathcal{D}$$, then there exists a distinguished triangle $$X \to A \to Y[-1] \to X[1]$$ such that X is an object of $$\mathcal{D}^{\le 0}$$ and Y is an object of $$\mathcal{D}^{\ge 0}$$.

Suppose that $$(\mathcal{D}^{\le 0}, \mathcal{D}^{\ge 0})$$ is a t-structure on $$\mathcal{D}$$. In this case, for any integer n, we define $$\mathcal{D}^{\le n}$$ to be the full subcategory of $$\mathcal{D}$$ whose objects have the form $$X[-n]$$, where $$X$$ is an object of $$\mathcal{D}^{\le 0}$$. Similarly, $$\mathcal{D}^{\ge n}$$ is the full subcategory of objects $$Y[-n]$$, where $$Y$$ is an object of $$\mathcal{D}^{\ge 0}$$. More briefly, we define
 * $$\begin{align}

\mathcal{D}^{\le n} &= \mathcal{D}^{\le 0}[-n], \\ \mathcal{D}^{\ge n} &= \mathcal{D}^{\ge 0}[-n]. \end{align}$$ With this notation, the axioms above may be rewritten as:
 * 1) If X is an object of $$\mathcal{D}^{\le 0}$$ and Y is an object of $$\mathcal{D}^{\ge 1}$$, then $$\operatorname{Hom}_{\mathcal{D}}(X, Y) = 0.$$
 * 2) $$\mathcal{D}^{\le 0} \subseteq \mathcal{D}^{\le 1}$$ and $$\mathcal{D}^{\ge 0} \supseteq \mathcal{D}^{\ge 1}$$.
 * 3) If A is an object of $$\mathcal{D}$$, then there exists a distinguished triangle $$X \to A \to Y \to X[1]$$ such that X is an object of $$\mathcal{D}^{\le 0}$$ and Y is an object of $$\mathcal{D}^{\ge 1}$$.

The heart or core of the t-structure is the full subcategory $$\mathcal{D}^\heartsuit$$ consisting of objects contained in both $$\mathcal{D}^{\le 0}$$ and $$\mathcal{D}^{\ge 0}$$, that is,
 * $$\mathcal{D}^\heartsuit = \mathcal{D}^{\le 0} \cap \mathcal{D}^{\ge 0}.$$

The heart of a t-structure is an abelian category (whereas a triangulated category is additive but almost never abelian), and it is stable under extensions.

A triangulated category with a choice of t-structure is sometimes called a t-category.

Variations
It is clear that, to define a t-structure, it suffices to fix integers m and n and specify $$\mathcal{D}^{\le m}$$ and $$\mathcal{D}^{\ge n}$$. Some authors define a t-structure to be the pair $$(\mathcal{D}^{\le 0}, \mathcal{D}^{\ge 1})$$.

The two subcategories $$\mathcal{D}^{\le 0}$$ and $$\mathcal{D}^{\ge 1}$$ determine each other. An object X is in $$\mathcal{D}^{\le 0}$$ if and only if $$\operatorname{Hom}(X, Y) = 0$$ for all objects Y in $$\mathcal{D}^{\ge 1}$$, and vice versa. That is, $$(\mathcal{D}^{\le 0}, \mathcal{D}^{\ge 1})$$ are left and right orthogonal complements of each other. Consequently, it is enough to specify only one of $$\mathcal{D}^{\le 0}$$ and $$\mathcal{D}^{\ge 1}$$. Moreover, because these subcategories are full by definition, it is enough to specify their objects.

The above notation is adapted to the study of cohomology. When the goal is to study homology, slightly different notation is used. A homological t-structure on $$\mathcal{D}$$ is a pair $$(\mathcal{D}_{\ge 0}, \mathcal{D}_{\le 0})$$ such that, if we define
 * $$(\mathcal{D}^{\le 0}, \mathcal{D}^{\ge 0}) = (\mathcal{D}_{\ge 0}, \mathcal{D}_{\le 0}),$$

then $$(\mathcal{D}^{\leq 0}, \mathcal{D}^{\geq 0})$$ is a (cohomological) t-structure on $$\mathcal{D}$$. That is, the definition is the same except that upper indices are converted to lower indices and the roles of $$\ge$$ and $$\le$$ are swapped. If we define
 * $$\begin{align}

\mathcal{D}_{\ge n} &= \mathcal{D}_{\ge 0}[n], \\ \mathcal{D}_{\le n} &= \mathcal{D}_{\le 0}[n], \end{align}$$ then the axioms for a homological t-structure may be written explicitly as
 * 1) If X is an object of $$\mathcal{D}_{\ge 0}$$ and Y is an object of $$\mathcal{D}_{\le -1}$$, then $$\operatorname{Hom}_{\mathcal{D}}(X, Y) = 0.$$
 * 2) $$\mathcal{D}_{\ge 1} \subseteq \mathcal{D}_{\ge 0}$$ and $$\mathcal{D}_{\le 1} \supseteq \mathcal{D}_{\le 0}$$.
 * 3) If A is an object of $$\mathcal{D}$$, then there exists a distinguished triangle $$X \to A \to Y \to X[1]$$ such that X is an object of $$\mathcal{D}_{\ge 0}$$ and Y is an object of $$\mathcal{D}_{\le -1}$$.

The natural t-structure
The most fundamental example of a t-structure is the natural t-structure on a derived category. Let $$\mathcal{A}$$ be an abelian category, and let $$D(\mathcal{A})$$ be its derived category. Then the natural t-structure is defined by the pair of subcategories
 * $$\begin{align}

D(\mathcal{A})^{\le 0} &= \{X \colon \forall i > 0,\ H^i(X) = 0\}, \\ D(\mathcal{A})^{\ge 0} &= \{X \colon \forall i < 0,\ H^i(X) = 0\}. \end{align}$$ It follows immediately that
 * $$\begin{align}

D(\mathcal{A})^{\le n} &= \{X \colon \forall i > n,\ H^i(X) = 0\}, \\ D(\mathcal{A})^{\ge n} &= \{X \colon \forall i < n,\ H^i(X) = 0\}, \\ D(\mathcal{A})^\heartsuit &= \{X \colon \forall i \neq 0,\ H^i(X) = 0\} \cong \mathcal{A}. \end{align}$$ In this case, the third axiom for a t-structure, the existence of a certain distinguished triangle, can be made explicit as follows. Suppose that $$A^\bullet$$ is a cochain complex with values in $$\mathcal{A}$$. Define
 * $$\begin{align}

\tau^{\le 0}A^\bullet &= (\cdots \to A^{-2} \to A^{-1} \to \ker d^0 \to 0 \to 0 \to \cdots), \\ \tau^{\ge 1}A^\bullet &= (\cdots \to 0 \to 0 \to A^0 / \ker d^0 \to A^1 \to A^2 \to \cdots). \end{align}$$ It is clear that $$\tau^{\ge 1}A^\bullet = A^\bullet / \tau^{\le 0}A^\bullet$$ and that there is a short exact sequence of complexes
 * $$0 \to \tau^{\le 0} A^\bullet \to A^\bullet \to \tau^{\ge 1} A^\bullet \to 0.$$

This exact sequence furnishes the required distinguished triangle.

This example can be generalized to exact categories (in the sense of Quillen). There are also similar t-structures for the bounded, bounded above, and bounded below derived categories. If $$\mathcal{C}$$ is an abelian subcategory of $$\mathcal{A}$$, then the full subcategory $$D_{\mathcal{C}}(\mathcal{A})$$ of $$D(\mathcal{A})$$ consisting of those complexes whose cohomology is in $$\mathcal{C}$$ has a similar t-structure whose heart is $$\mathcal{C}$$.

Perverse sheaves
The category of perverse sheaves is, by definition, the core of the so-called perverse t-structure on the derived category of the category of sheaves on a complex analytic space X or (working with l-adic sheaves) an algebraic variety over a finite field. As was explained above, the heart of the standard t-structure simply contains ordinary sheaves, regarded as complexes concentrated in degree 0. For example, the category of perverse sheaves on a (possibly singular) algebraic curve X (or analogously a possibly singular surface) is designed so that it contains, in particular, objects of the form
 * $$i_* F_Z, j_* F_U[1]$$

where $$i: Z \to X$$ is the inclusion of a point, $$F_Z$$ is an ordinary sheaf, $$U$$ is a smooth open subscheme and $$F_U$$ is a locally constant sheaf on U. Note the presence of the shift according to the dimension of Z and U respectively. This shift causes the category of perverse sheaves to be well-behaved on singular spaces. The simple objects in this category are the intersection cohomology sheaves of subvarieties with coefficients in an irreducible local system. This t-structure was introduced by Beilinson, Bernstein and Deligne. It was shown by Beilinson that the derived category of the heart $$D^b(Perv(X))$$ is in fact equivalent to the original derived category of sheaves. This is an example of the general fact that a triangulated category may be endowed with several distinct t-structures.

Graded modules
A non-standard example of a t-structure on the derived category of (graded) modules over a graded ring has the property that its heart consists of complexes
 * $$\dots \to P^n \to P^{n+1} \to \dots$$

where $$P^n$$ is a module generated by its (graded) degree n. This t-structure called geometric t-structure plays a prominent role in Koszul duality.

Spectra
The category of spectra is endowed with a t-structure generated, in the sense above, by a single object, namely the sphere spectrum. The category $$Sp^{\le 0}$$ is the category of connective spectra, i.e., those whose negative homotopy groups vanish. (In areas related to homotopy theory, it is common to use homological conventions, as opposed to cohomological ones, so in this case it is common to replace "$$\le$$" (superscript) by "$$\ge$$" (subscript). Using this convention, the category of connective spectra is denoted as $$Sp_{\ge 0}$$.)

Motives
A conjectural example in the theory of motives is the so-called motivic t-structure. Its (conjectural) existence is closely related to certain standard conjectures on algebraic cycles and vanishing conjectures, such as the Beilinson-Soulé conjecture.

Truncation functors
In the above example of the natural t-structure on the derived category of an abelian category, the distinguished triangle guaranteed by the third axiom was constructed by truncation. As operations on the category of complexes, the truncations $$\tau_{\le 0}A^\bullet$$ and $$\tau_{\ge 1} A^\bullet$$ are functorial, and the resulting short exact sequence of complexes is natural in $$A^\bullet$$. Using this, it can be shown that there are truncation functors on the derived category and that they induce a natural distinguished triangle.

In fact, this is an example of a general phenomenon. While the axioms for a t-structure do not assume the existence of truncation functors, such functors can always be constructed and are essentially unique. Suppose that $$\mathcal{D}$$ is a triangulated category and that $$(\mathcal{D}^{\le 0}, \mathcal{D}^{\ge 0})$$ is a t-structure. The precise statement is that the inclusion functors
 * $$\begin{align}

\iota^{\le n} \colon &\mathcal{D}^{\le n} \to \mathcal{D}, \\ \iota^{\ge n} \colon &\mathcal{D}^{\ge n} \to \mathcal{D} \end{align}$$ admit adjoints. These are functors
 * $$\begin{align}

\tau^{\le n} \colon &\mathcal{D} \to \mathcal{D}^{\le n}, \\ \tau^{\ge n} \colon &\mathcal{D} \to \mathcal{D}^{\ge n} \end{align}$$ such that
 * $$\begin{align}

\iota^{\le n} \dashv \tau^{\le n}, \\ \tau^{\ge n} \dashv \iota^{\ge n}. \end{align}$$ Moreover, for any object $$A$$ of $$\mathcal{D}$$, there exists a unique
 * $$d \in \operatorname{Hom}^1(\tau^{\ge 1} A, \tau^{\le 0} A)$$

such that d and the counit and unit of the adjunctions together define a distinguished triangle
 * $$\tau^{\le 0} A \to A \to \tau^{\ge 1} A\ \stackrel{d}{\to}\ \tau^{\le 0} A[1].$$

Up to unique isomorphism, this is the unique distinguished triangle of the form $$X \to A \to Y \to X[1]$$ with $$X$$ and $$Y$$ objects of $$\mathcal{D}^{\le 0}$$ and $$\mathcal{D}^{\ge 1}$$, respectively. It follows from the existence of this triangle that an object $$A$$ lies in $$\mathcal{D}^{\le n}$$ (resp. $$\mathcal{D}^{\ge n}$$) if and only if $$\tau^{\ge n+1}(A) = 0$$ (resp. $$\tau^{\le n-1}(A) = 0$$).

The existence of $$\tau^{\le 0}$$ implies the existence of the other truncation functors by shifting and taking opposite categories. If $$A$$ is an object of $$\mathcal{D}$$, the third axiom for a t-structure asserts the existence of an $$X$$ in $$\mathcal{D}^{\le 0}$$ and a morphism $$X \to A$$ fitting into a certain distinguished triangle. For each $$A$$, fix one such triangle and define $$\tau^{\le 0}(A) = X$$. The axioms for a t-structure imply that, for any object $$T$$ of $$\mathcal{D}^{\le 0}$$, we have
 * $$\operatorname{Hom}(T, X) \cong \operatorname{Hom}(T, A),$$

with the isomorphism being induced by the morphism $$X \to A$$. This exhibits $$X$$ as a solution to a certain universal mapping problem. Standard results on adjoint functors now imply that $$X$$ is unique up to unique isomorphism and that there is a unique way to define $$\tau^{\le 0}$$ on morphisms that makes it a right adjoint. This proves the existence of $$\tau^{\le 0}$$ and hence the existence of all the truncation functors.

Repeated truncation for a t-structure behaves similarly to repeated truncation for complexes. If $$n \le m$$, then there are natural transformations
 * $$\begin{align}

\tau^{\le n} &\to \tau^{\le m}, \\ \tau^{\ge n} &\to \tau^{\ge m}, \end{align}$$ which yield natural equivalences
 * $$\begin{align}

\tau^{\le n}\ &\stackrel{\sim}{\to}\ \tau^{\le n} \circ \tau^{\le m}, \\ \tau^{\ge m}\ &\stackrel{\sim}{\to}\ \tau^{\ge m} \circ \tau^{\ge n}, \\ \tau^{\ge n} \circ \tau^{\le m} \ &\stackrel{\sim}{\to}\ \tau^{\le m} \circ \tau^{\ge n}. \end{align}$$

Cohomology functors
The nth cohomology functor $$H^n$$ is defined as
 * $$H^n = \tau^{\le 0} \circ \tau^{\ge 0} \circ [n].$$

As the name suggests, this is a cohomological functor in the usual sense for a triangulated category. That is, for any distinguished triangle $$X \to Y \to Z \to X[1]$$, we obtain a long exact sequence
 * $$\cdots \to H^i(X) \to H^i(Y) \to H^i(Z) \to H^{i + 1}(X) \to \cdots.$$

In applications to algebraic topology, the cohomology functors may be denoted $$\pi_n$$ instead of $$H^n$$. The cohomology functors take values in the heart $$\mathcal{D}^\heartsuit$$. By one of the repeated truncation identities above, up to natural equivalence it is equivalent to define
 * $$H^n = \tau^{\ge 0} \circ \tau^{\le 0} \circ [n].$$

For the natural t-structure on a derived category $$D(\mathcal{A})$$, the cohomology functor $$H^n$$ is, up to quasi-isomorphism, the usual nth cohomology group of a complex. However, considered as functors on complexes, this is not true. Consider, for example, $$H^0$$ as defined in terms of the natural t-structure. By definition, this is
 * $$\begin{align}

H^0(A^\bullet) &= \tau^{\le 0}(\tau^{\ge 0}(A^\bullet)) \\ &= \tau^{\le 0}(\cdots \to 0 \to A^{-1} / \ker d^{-1} \to A^0 \to A^1 \to \cdots) \\ &= (\cdots \to 0 \to A^{-1} / \ker d^{-1} \to \ker d^0 \to 0 \to \cdots). \end{align}$$ This complex is non-zero in degrees $$-1$$ and $$0$$, so it is clearly not the same as the zeroth cohomology group of the complex $$A^\bullet$$. However, the non-trivial differential is an injection, so the only non-trivial cohomology is in degree $$0$$, where it is $$\ker d^0 / \operatorname{im} d^{-1}$$, the zeroth cohomology group of the complex $$A^\bullet$$. It follows that the two possible definitions of $$H^0(A^\bullet)$$ are quasi-isomorphic.

A t-structure is non-degenerate if the intersection of all $$\mathcal{D}^{\le n}$$, as well as the intersection of all $$\mathcal{D}^{\ge n}$$, consists only of zero objects. For a non-degenerate t-structure, the collection of functors $$\{H^n\}_{n \in \mathbf{Z}}$$ is conservative. Moreover, in this case, $$\mathcal{D}^{\le n}$$ (resp. $$\mathcal{D}^{\ge n}$$) may be identified with the full subcategory of those objects $$A$$ for which $$H^i(A) = 0$$ for $$i > n$$ (resp. $$i < n$$).

Exact functors
For $$i = 1, 2$$, let $$\mathcal{D}_i$$ be a triangulated category with a fixed t-structure $$(\mathcal{D}_i^{\le 0}, \mathcal{D}_i^{\ge 0})$$. Suppose that $$F \colon \mathcal{D}_1 \to \mathcal{D}_2$$ is an exact functor (in the usual sense for triangulated categories, that is, up to a natural equivalence it commutes with translation and preserves distinguished triangles). Then $$F$$ is:
 * Left t-exact if $$F(\mathcal{D}_1^{\ge 0}) \subseteq \mathcal{D}_2^{\ge 0}$$,
 * Right t-exact if $$F(\mathcal{D}_1^{\le 0}) \subseteq \mathcal{D}_2^{\le 0}$$, and
 * t-exact if it is both left and right t-exact.

It is elementary to see that if $$F$$ is fully faithful and t-exact, then an object $$A$$ of $$\mathcal{D}_1$$ is in $$\mathcal{D}_1^{\le 0}$$ (resp. $$\mathcal{D}_1^{\ge 0}$$) if and only if $$FA$$ is in $$\mathcal{D}_2^{\le 0}$$ (resp. $$\mathcal{D}_2^{\ge 0}$$). It is also elementary to see that if $$G \colon \mathcal{D}_2 \to \mathcal{D}_3$$ is another left (resp. right) t-exact functor, then the composite $$G \circ F$$ is also left (resp. right) t-exact.

The motivation for the study of one-sided t-exactness properties is that they lead to one-sided exactness properties on hearts. Let $$\iota_i^\heartsuit \colon \mathcal{D}_i^\heartsuit \to \mathcal{D}_i$$ be the inclusion. Then there is a composite functor
 * $${}^pF = H^0 \circ F \circ \iota_1^\heartsuit \colon \mathcal{D}_1^\heartsuit \to \mathcal{D}_2^\heartsuit.$$

It can be shown that if $$F$$ is left (resp. right) exact, then $${}^pF$$ is also left (resp. right) exact, and that if $$G$$ is also left (resp. right) exact, then $${}^p(G \circ F) = ({}^pG) \circ ({}^pF)$$.

If $$F$$ is right (resp. left) t-exact, and if $$A$$ is in $$\mathcal{D}^{\le 0}$$ (resp. $$\mathcal{D}^{\ge 0}$$), then there is a natural isomorphism $${}^pF(H^0A)\ \stackrel{\sim}{\to}\ H^0F(A)$$ (resp. $$H^0F(A)\ \stackrel{\sim}{\to}\ {}^pF(H^0A)$$).

If $$(T^*, T_*) \colon \mathcal{D}_1 \leftrightarrows \mathcal{D}_2$$ are exact functors with $$T^*$$ left adjoint to $$T_*$$, then $$T^*$$ is right t-exact if and only if $$T_*$$ is left t-exact, and in this case, $$({}^pT^*, {}^pT_*)$$ are a pair of adjoint functors $$\mathcal{D}_1^\heartsuit \leftrightarrows \mathcal{D}_2^\heartsuit$$.

Constructions of t-structures
Let $$(\mathcal{D}^{\le 0}, \mathcal{D}^{\ge 0})$$ be a t-structure on $$\mathcal{D}$$. If n is an integer, then the translation by n t-structure is $$(\mathcal{D}^{\le n}, \mathcal{D}^{\ge n})$$. The dual t-structure is the t-structure on the opposite category $$\mathcal{D}^\text{op}$$ defined by $$((\mathcal{D}^{\ge 0})^\text{op}, (\mathcal{D}^{\le 0})^\text{op})$$.

Let $$\mathcal{D}'$$ be a triangulated subcategory of a triangulated category $$\mathcal{D}$$. If $$(\mathcal{D}^{\le 0}, \mathcal{D}^{\ge 0})$$ is a t-structure on $$\mathcal{D}$$, then
 * $$((\mathcal{D}')^{\le 0}, (\mathcal{D}')^{\ge 0}) = (\mathcal{D}' \cap \mathcal{D}^{\le 0}, \mathcal{D}' \cap \mathcal{D}^{\ge 0})$$

is a t-structure on $$\mathcal{D}'$$ if and only if $$\mathcal{D}'$$ is stable under the truncation functor $$\tau^{\le 0}$$. When this condition holds, the t-structure $$((\mathcal{D}')^{\le 0}, (\mathcal{D}')^{\ge 0})$$ is called the induced t-structure. The truncation and cohomology functors for the induced t-structure are the restriction to $$\mathcal{D}'$$ of those on $$\mathcal{D}$$. Consequently, the inclusion of $$\mathcal{D}'$$ in $$\mathcal{D}$$ is t-exact, and $$(\mathcal{D}')^\heartsuit = \mathcal{D}^\heartsuit \cap \mathcal{D}'$$.

To construct the category of perverse sheaves, it is important to be able to define a t-structure on a category of sheaves over a space by working locally in that space. The precise conditions necessary for this to be possible can be abstracted somewhat to the following setup. Suppose that there are three triangulated categories and two morphisms
 * $$\mathcal{D}_F\ \stackrel{i_*}{\to}\ \mathcal{D}\ \stackrel{j^*}{\to}\ \mathcal{D}_U$$

satisfying the following properties.
 * There are two sequences of triples of adjoint functors $$(j_!, j^*, j_*)$$ and $$(i^*, i_*, i^!)$$.
 * The functors $$i_*$$, $$j_!$$, and $$j^*$$ are full and faithful, and they satisfy $$j^*i_* = 0$$.
 * There are unique differentials making, for every K in $$\mathcal{D}$$, exact triangles
 * $$\begin{align}

j_!j^*K &\to K \to i_*i^*K \to j_!j^*K[1], \\ i_*i^!K &\to K \to j_*j^*K \to i_*i^!K[1]. \end{align}$$ In this case, given t-structures $$(\mathcal{D}_U^{\le 0}, \mathcal{D}_U^{\ge 0})$$ and $$(\mathcal{D}_F^{\le 0}, \mathcal{D}_F^{\ge 0})$$ on $$\mathcal{D}_U$$ and $$\mathcal{D}_F$$, respectively, there is a t-structure on $$\mathcal{D}$$ defined by
 * $$\begin{align}

\mathcal{D}^{\le 0} &= \{ K \in \mathcal{D} \colon j^*K \in \mathcal{D}_U^{\le 0},\ i^*K \in \mathcal{D}_F^{\le 0}\}, \\ \mathcal{D}^{\ge 0} &= \{ K \in \mathcal{D} \colon j^*K \in \mathcal{D}_U^{\ge 0},\ i^!K \in \mathcal{D}_F^{\ge 0}\}. \end{align}$$ This t-structure is said to be the gluing of the t-structures on U and F. The intended use cases are when $$\mathcal{D}$$, $$\mathcal{D}_U$$, and $$\mathcal{D}_F$$ are bounded below derived categories of sheaves on a space X, an open subset U, and the closed complement F of U. The functors $$j^*$$ and $$i_*$$ are the usual pullback and pushforward functors. This works, in particular, when the sheaves in question are left modules over a sheaf of rings $$\mathcal{O}$$ on X and when the sheaves are ℓ-adic sheaves.

Many t-structures arise by means of the following fact: in a triangulated category with arbitrary direct sums, and a set $$S_0$$ of compact objects in $$\mathcal{D}$$, the subcategories
 * $$\begin{align}

\mathcal{D}^{\ge 1} &= \{X \in \mathcal{D} \colon \operatorname{Hom}(S_0[-n], X) = 0, n \ge 0\}, \\ \mathcal{D}^{\le 0} &= \{Y \in \mathcal{D} \colon \operatorname{Hom}(Y, \mathcal{D}^{\ge 1}) = 0\}, \end{align}$$ can be shown to be a t-structure. The resulting t-structure is said to be generated by $$S_0$$.

Given an abelian subcategory $$\mathcal{C}$$ of a triangulated category $$\mathcal{D}$$, it is possible to construct a subcategory of $$\mathcal{D}$$ and a t-structure on that subcategory whose heart is $$\mathcal{C}$$.

On stable ∞-categories
The elementary theory of t-structures carries over to the case of ∞-categories with few changes. Let $$\mathcal{D}$$ be a stable ∞-category. A t-structure on $$\mathcal{D}$$ is defined to be a t-structure on its homotopy category $$\mathrm{h}\mathcal{D}$$ (which is a triangulated category). A t-structure on an ∞-category can be notated either homologically or cohomologically, just as in the case of a triangulated category.

Suppose that $$\mathcal{D}$$ is an ∞-category with homotopy category $$\mathrm{h}\mathcal{D}$$ and that $$(\mathrm{h}\mathcal{D}_{\ge 0}, \mathrm{h}\mathcal{D}_{\le 0})$$ is a t-structure on $$\mathrm{h}\mathcal{D}$$. Then, for each integer n, we define $$\mathcal{D}_{\ge n}$$ and $$\mathcal{D}_{\le n}$$ to be the full subcategories of $$\mathcal{D}$$ spanned by the objects in $$\mathrm{h}\mathcal{D}_{\ge n}$$ and $$\mathrm{h}\mathcal{D}_{\le n}$$, respectively. Define
 * $$\begin{align}

\iota_{\ge n} &\colon \mathcal{D}_{\ge n} \to \mathcal{D}, \\ \iota_{\le n} &\colon \mathcal{D}_{\le n} \to \mathcal{D} \end{align}$$ to be the inclusion functors. Just as in the case of a triangulated category, these admit a right and a left adjoint, respectively, the truncation functors
 * $$\begin{align}

\tau_{\ge n} &\colon \mathcal{D} \to \mathcal{D}_{\ge n}, \\ \tau_{\le n} &\colon \mathcal{D} \to \mathcal{D}_{\le n} \end{align}$$ These functors satisfy the same repeated truncation identities as in the triangulated category case.

The heart of a t-structure on $$\mathcal{D}$$ is defined to be the ∞-subcategory $$\mathcal{D}^\heartsuit = \mathcal{D}_{\ge 0} \cap \mathcal{D}_{\le 0}$$. The category $$\mathcal{D}^\heartsuit$$ is equivalent to the nerve of its homotopy category $$\mathrm{h}\mathcal{D}^\heartsuit$$. The cohomology functor $$\pi_n$$ is defined to be $$\tau_{\ge 0} \circ \tau_{\le 0} \circ [-n]$$, or equivalently $$\tau_{\le 0} \circ \tau_{\ge 0} \circ [-n]$$.

The existence of $$\tau_{\le n}$$ means that $$\iota_{\le n}$$ is, by definition, a localization functor. In fact, there is a bijection between t-structures on $$\mathcal{D}$$ and certain kinds of localization functors called t-localizations. These are localization functors L whose essential image is closed under extension, meaning that if $$X \to Y \to Z$$ is a fiber sequence with X and Z in the essential image of L, then Y is also in the essential image of L. Given such a localization functor L, the corresponding t-structure is defined by
 * $$\begin{align}

\mathcal{D}_{\ge 0} &= \{A \colon LA \simeq 0\}, \\ \mathcal{D}_{\le -1} &= \{A \colon LA \simeq A\}. \end{align}$$ t-localization functors can also be characterized in terms of the morphisms f for which Lf is an equivalence. A set of morphisms S in an ∞-category $$\mathcal{D}$$ is quasisaturated if it contains all equivalences, if any 2-simplex in $$\mathcal{D}$$ with two of its non-degenerate edges in S has its third non-degenerate edge in S, and if it is stable under pushouts. If $$L \colon \mathcal{D} \to \mathcal{D}$$ is a localization functor, then the set S of all morphisms f for which Lf is an equivalence is quasisaturated. Then L is a t-localization functor if and only if S is the smallest quasisaturated set of morphisms containing all morphisms $$\{0 \to X \colon LX \simeq 0\}$$.

The derived category of an abelian category has several subcategories corresponding to different boundedness conditions. A t-structure on a stable ∞-category can be used to construct similar subcategories. Specifically,
 * $$\begin{align}

\mathcal{D}_+ &= \bigcup_{n \in \mathbf{Z}} \mathcal{D}_{\le n}, \\ \mathcal{D}_- &= \bigcup_{n \in \mathbf{Z}} \mathcal{D}_{\ge n}, \\ \mathcal{D}_b &= \mathcal{D}_+ \cap \mathcal{D}_-. \end{align}$$ These are stable subcategories of $$\mathcal{D}$$. One says that $$\mathcal{D}$$ is left bounded (with respect to the given t-structure) if $$\mathcal{D} = \mathcal{D}_+$$, right bounded if $$\mathcal{D} = \mathcal{D}_-$$, and bounded if $$\mathcal{D} = \mathcal{D}_b$$.

It is also possible to form a left or right completion with respect to a t-structure. This is analogous to formally adjoining directed limits or directed colimits. The left completion $$\hat\mathcal{D}$$ of $$\mathcal{D}$$ is the homotopy limit of the diagram
 * $$\cdots \to \mathcal{D}_{\le 2}\ \stackrel{\tau_{\le 1}}{\to}\ \mathcal{D}_{\le 1}\ \stackrel{\tau_{\le 0}}{\to}\ \mathcal{D}_{\le 0}\ \stackrel{\tau_{\le -1}}{\to}\ \cdots.$$

The right completion is defined dually. The left and right completions are themselves stable ∞-categories which inherit a canonical t-structure. There is a canonical map from $$\mathcal{D}$$ to either of its completions, and this map is t-exact. We say that $$\mathcal{D}$$ is left complete or right complete if the canonical map to its left or right completion, respectively, is an equivalence.

Related concepts
If the requirement $$D^{\le 0}\subset D^{\le 1}$$, $$D^{\ge 1}\subset D^{\ge 0};$$ is replaced by the opposite inclusion
 * $$D^{\le 0}\supset D^{\le 1}$$, $$D^{\ge 1}\supset D^{\ge 0},$$

and the other two axioms kept the same, the resulting notion is called a co-t-structure or weight structure.

title: T-structure


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Wikipedia:Featured article candidates/Elagabalus

Elagabalus
This is largely a self nom as I rewrote and expanded the article in late March from an existing version. It has relevant pictures, references, external links and well divided sections and subsections. It has been stable since it was rewritten in March. -JCarriker 06:49, Apr 26, 2005 (UTC)
 * It seems OK. I'm neutral, wish it had more detail. I went through and did some minor copyediting here and there. Everyking 13:39, 26 Apr 2005 (UTC)
 * May I ask what sort of details you would like to see? Perhaps I can try to improve what you think is missing, though I think you'd be hard pressed to find a more detailed account that doesn't make heavy use of the Historia Augusta as absolute truth. Please also keep in mind that this is a rather obscure historical figure whose memory was intentionally blackened and suffered a decree of Damnatio memoriae. -JCarriker 14:50, Apr 26, 2005 (UTC)
 * Just because you say the Historia Augusta says something doesn't mean you need to treat it as absolute truth. A thoroughly comprehensive article here would mention all the known details of his life, all the uncertain things from the sources, and also discuss the various historical views of him up to the present day. Everyking 14:59, 26 Apr 2005 (UTC)
 * There are quotes that do that, however I disagree that all the known or alleged details of his life should be included. Only the most important and relevant inforation should be included in the main article, detail is wonderful to have-- but you can have to much of a good thing). Perhaps a subarticle could be created to provide the controversies surrounding him in greater detail. I believe the current article provides a good thorough, but concise bio. I do appreciate your opinion though. Thanks. -JCarriker 15:20, Apr 26, 2005 (UTC)
 * Well, I certainly wouldn't object if it were in a subarticle, but I wouldn't worry about a subarticle until the main article grows to a certain point. Everyking 15:46, 26 Apr 2005 (UTC)
 * Support: I like this version very much. I remembering a time when i thought that this article was a mess beyhond any salvation. I was wrong! muriel@pt 14:08, 26 Apr 2005 (UTC)
 * Somewhere in this article there should be a derivations/explanations for the names "Elagabalus" and "Heliogabalus", presumably consistent with Elagabalus Sol Invictus. Paul August ☎ 14:43, Apr 26, 2005 (UTC)
 * I'm not sure what you mean. There is an derivations/explanations under the section Origin of his name. Please elaborate. -JCarriker 14:50, Apr 26, 2005 (UTC)
 * OK sorry I missed that. Perhaps something could be said about it in the lead? Paul August ☎ 15:05, Apr 26, 2005 (UTC)
 * That's fine with me. Perhaps as an adendum to where the derivation of the god's name is described such as which is also from were his name is derived. -JCarriker 15:20, Apr 26, 2005 (UTC)
 * Support. Very interesting read.  Acegikmo1 16:15, 26 Apr 2005 (UTC)
 * Support, although now that I have the time I would like to add some details to the historiography of Elagabalus:
 * The Historia Augusta has been argued to be of uneven reliability, the earlier articles being based on the now-lost work of Marius Maximus (which is reliable), & the later on the author's idiosyncratic imagination; so to say that the entire work is "unreliable" is an oversimplification. The section on Elagabalus is a mixure of the two, according to a 1970 article by T.D. Barnes, where he is said to have marked the parts based on Marius.

 * Anthony Birley has translated the section of the Historia Augusta for Penguin, & supplied useful notes for this & the rest of the book. It deserves to be mentioned in the sources.

 * I think it's the right thing to first ask to make important changes like these at this point, rather than to be bold & edit. -- llywrch 18:24, 26 Apr 2005 (UTC)
 * Please feel free to make the changes. -JCarriker 00:09, Apr 27, 2005 (UTC)

 * object for most of your references it's not clear how they were used and it's not clear which sections should be looked up in which references. Please could you add some inline references.  I made the one external link into a link with full bibliographic information. Mozzerati 06:51, 2005 Apr 27 (UTC)
 * I don't think I have the syntax expertise to do so personally and I don't think I'd enjoy doing it either. I can help you crate them by providing the information. For what parts would you like to see inline refs? -JCarriker 20:28, Apr 27, 2005 (UTC)
 * In line references are neither mandatory nor a specific obligation of FACs. They are also, in my opinion, pedantic in the context of wikipedia. muriel@pt 10:26, 28 Apr 2005 (UTC)
 * Actually that's incorrect. Direct from the criteria: "Include references, arranged in a ==References== section and enhanced by the appropriate use of inline citations.". They are important for the reasons Mozzerati mentions, and just to support the goals of the Verifiability policy. "Appropriate" is open to interpretation, but certainly means some, not none. The general consensus seems to be that important and potentially contentious points should be cited to a reliable source. JCarriker, I'll help with the syntax if you like, but you can use Template talk:Inote or something like Footnote3 to make it easier on you. Oh yeah, I do see one. More like that would be fine. - Taxman 20:43, May 3, 2005 (UTC)
 * Inline references Taxman, of course i'm not questioning the presence of a Reference section. muriel@pt 13:58, 5 May 2005 (UTC)
 * There is a rather good reference section in the article. The only material that is truly controversial to scholars is the transexual ref. The other informationis widely accepted and well known as far as scholarship in relation to Elagabalus goes. The quotes are properly attributed, and to give them inline refs would be redundant. If you have something specifically in mind for one, I'll be happy to give you the source so you can make an inlineref. -JCarriker 19:43, May 5, 2005 (UTC)

Comment as of 16:26, May 3, 2005 (UTC) 19:43, May 5, 2005 (UTC) this is the vote tally correct?
 * Support.- JCarriker
 * Neutral.- Everyking
 * Support.- muriel
 * Comment.- Paul August
 * Support.- Acegikmo1
 * Support.- Llywrch
 * Object.- Mozzerati
 * Support.- Pedro

Just checking. -JCarriker 16:26, May 3, 2005 (UTC) 19:43, May 5, 2005 (UTC)
 * support how interresting! This goes with something that I'm reading at the moment (The Roman Empire during Octavius rule), in which people married and diversorded has they changed their underware.The controversial area has already a proper reference, although I think it is really unnecessary. -Pedro 14:06, 4 May 2005 (UTC)

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


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User:Laubrau~enwiki

fr:User:Laubrau

title: User:Laubrau~enwiki


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Tava

A tava(h) / tawa(h) (mainly on the Indian subcontinent), saj (in Arabic), sac (in Turkish), and other variations and combinations thereof, is a metal-made cooking utensil. The tawa is round and can be flat, but more commonly has a curved profile, and while the concave side can be used as a wok or frying pan, the convex side is used for cooking flatbreads and pancakes.

The Indian tawa might have a handle or not, and it can be made of cast iron or aluminium, or of carbon steel. The utensil may be enameled or given a non-stick surface. The tawa and saj are used in the cuisines of South, Central, and West Asia, as well as of the Caucasus and the Balkans. The tawa is also used in Indo-Caribbean cuisine.

Taaba, Tava, tawa
In Iran, the Persian word tāve (تاوه) is used which is derived from the Persian word taaba which means something that is curved or tempered. The root word taab in Persian is a verb which means to bend or temper or curve (but see here-below for the use of saj in Iran). It is cognate with tawaa, a word which in nearly all Indo-Aryan languages such as Punjabi, Hindi and Urdu means cooking pan. In Afghanistan, the curved cast-iron utensil used for cooking bread is known as tawah, but in Pashto it is more popularly known as tabakhey (تبخے/طبخی). The Georgian cognate is tapa (ტაფა).

Saj, saç
Saj (صاج, lit. sheet-metal) is the equivalent of tava in Arabic, with the equivalent saç or sac in Turkish, and is used in Southwest Asia. In Iran, saj is used for the curved iron plate employed in cooking bread (but see here-above for the use of tāve in Iran).

Variants, change of meaning
The word tava is also used in Turkish and all across the Balkans, and refers to any kind of frying pan. In Serbia and Bulgaria however, a тава (tava) is a metal baking tray with raised margins (for the meaning of sach in those same countries, see here-below). In Romanian too, tava can mean baking tray, such as employed for baking in an oven, but it can also mean tray, such as used for serving food and drink.

The sač is a saj-shaped lid used as a cooking utensil in the Balkans. In Serbia and Bulgaria, the flat ceramic сач (sach) or сачѐ (sachè) is used for table-top cooking of thin slices of vegetables and meat (for the meaning of tava in those same countries, see here-above).

Uses
A tava or saj is used to bake a variety of leavened and unleavened flatbreads and pancakes across the broad region: pita, naan, saj bread, roti, chapati, paratha, dosa, and pesarattu. In Pakistan, especially in rural areas, large convex saj are used to cook several breads at the same time or to make rumali roti.

title: Tava


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Wikipedia:Articles for deletion/Izziehugger

 This page is an archive of the discussion about the proposed deletion of the article below. This page is no longer live. Further comments should be made on the article's talk page rather than here so that this page is preserved as an historic record. The result of the debate was delete. — Xezbeth 18:55, May 11, 2005 (UTC)

Izziehugger
Article created by LevelCheck, based on an invented term authored by a usenet troll named Matt Giwer to describe people who like Israel. Google test returns about 6 hits, most likely related to message board postings by Giwer himself. --Viriditas | Talk 06:59, 26 Apr 2005 (UTC)
 * Delete. Another disruptive article creation.  Completely and obviously non-notable. Jayjg (talk)  07:10, 26 Apr 2005 (UTC)
 * I've dealt with Matt Giwer before on Usenet. He's an anti-Semitic Holocaust-denier, and apparently a prolific enough one to rate his own page on the Nizkor Project. Giwer himself might be notable enough to rate an article (he doesn't have one currently) but his nasty little neologisms aren't. Anyway, delete. Firebug
 * In that case I vote to Merge into an article on Matt Giwer anyone who makes it to nizkor projects list of kooks is notable. Klonimus 07:39, 4 May 2005 (UTC)
 * Delete orig research.  ←Humus sapiens←Talk 07:47, 26 Apr 2005 (UTC)
 * Delete. This should really be a speedy delete. SlimVirgin (talk) 08:10, Apr 26, 2005 (UTC)
 * Delete. Neologism. -- 8^D gab 13:35, 2005 Apr 26 (UTC)
 * Delete — neither a particularly creative nor a historically-interesting expression. — RJH 15:36, 26 Apr 2005 (UTC)
 * Delete. Neologism, original research, disruptive. -- M P er el ( talk 15:39, Apr 26, 2005 (UTC)
 * Delete per RJHall. Samaritan 17:35, 26 Apr 2005 (UTC)
 * Should've been a speedy delete. No reasonable Wikipedian would have created this.  Postdlf 20:51, 26 Apr 2005 (UTC)
 * Please note that this page is being used as evidence in Requests for Arbitration's case on LevelCheck, which I proposed today--please don't delete until that case is finished, if it is accepted by the Arbcom. Meelar (talk) 21:08, Apr 26, 2005 (UTC)
 * Comment: I would rather use the diffs as evidence: they contain more details (such as author, date, etc) and are more reliable because they do not depend on subsequent edits.  ←Humus sapiens←Talk 08:02, 4 May 2005 (UTC)
 * Delete. As someone who's dealt with Matt Giwer (or a good impostor) on the POV-RAY newsgroups, I can confirm that he uses the word.  I can also confirm that he's just about the only person who does.  The term isn't significant enough for Wikipedia, and I doubt Wiktionary would want it. --Carnildo 21:44, 26 Apr 2005 (UTC)
 * Delete, as above. Unless it qualifies as a speedy, in which case do that! Master Thief Garrett 01:16, 27 Apr 2005 (UTC)
 * Delete, not every epithet is encyclopedic. And, someone wishing to CREATE a new epithet could simply salt the web with a few instances, then create a Wikipedia article like this.A2Kafir 16:03, 27 Apr 2005 (UTC)
 * Neologism whose usage is negligible. Delete. -- Hoary 02:56, 2005 May 10 (UTC)

 * This page is now preserved as an archive of the debate and, like some other VfD subpages, is no longer 'live'. Subsequent comments on the issue, the deletion, or the decision-making process should be placed on the relevant 'live' pages. Please do not edit this page.


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User talk:Susmitajay

Welcome!

Hello, and welcome to Wikipedia. Thank you for your contributions. I hope you like the place and decide to stay. Here are a few good links for newcomers: I hope you enjoy editing here and being a Wikipedian! By the way, you can sign your name on Talk and vote pages using three tildes, like this: ~~~. Four tildes (~~~~) produces your name and the current date. If you have any questions, see the help pages, add a question to the village pump or ask me on my Talk page. Again, welcome!
 * How to edit a page
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 * How to write a great article
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 * If you're ready for the complete list of Wikipedia documentation, there's also Topical index.

Zzyzx11 | Talk 06:53, 26 Apr 2005 (UTC)

title: User talk:Susmitajay


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Talk:Patriarch of All Romania

Untitled
I suggest that the biographical info in this article should be merged to already-existing Teoctist, and this article should focus on the institution of the Patriarch. Man vyi 06:58, 26 Apr 2005 (UTC)

This needs to fixed to a much higher standard

What?
After reading this article, I haven't got the slightest idea what it's really about. Someone should rewrite it. — Preceding unsigned comment added by 169.152.251.99 (talk • contribs) 16 November 2005 (UTC)

A Commons file used on this page or its Wikidata item has been nominated for deletion
The following Wikimedia Commons file used on this page or its Wikidata item has been nominated for deletion: Participate in the deletion discussion at the. —Community Tech bot (talk) 22:23, 16 October 2021 (UTC)
 * Patriarhul Daniel.jpg

title: Talk:Patriarch of All Romania


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Tanaka Hisashige

Hisashige Tanaka (田中 久重) was a Japanese businessman, inventor, mechanical engineer, and rangaku scholar who was prominent during the Bakumatsu and early Meiji period in Japan. In 1875, he founded what became the Toshiba Corporation. He has been called the "Thomas Edison of Japan" or "Karakuri Giemon."

Biography
Tanaka was born in Kurume, Chikugo province (present-day Fukuoka prefecture) as the eldest son of a tortoise shell craftsman. Apprenticed at an early age, he was a gifted artisan. At the age of eight, he invented an inkstone case with a secret lock, which required a cord to be twisted in a certain manner to open it. At the age of 14, he had invented a loom capable of weaving intricate designs into fabric. From age 20 he began to make karakuri puppet dolls, autonomous dolls powered by springs, pneumatics and hydraulics, capable of relatively complex movements, which were much in demand by the aristocrats of Kyoto, daimyō in feudal domains, and by the Shōgun's court in Edo. At age 21, he was performing around the country at festivals with clockwork dolls he constructed himself. He declined to take over the family business, surrendering his position to his younger brother and devoted his full attention to karakuri dolls. It is often said that the best masterpieces of his karakuri are Yumi-Hiki Doji (arrow-shooting boy) and Moji-kaki doll (letter-writing doll). In his mid-thirties, however, he aspired to invent more practical products. In 1834, he relocated to Osaka, where he experimented in pneumatics, hydraulics and forms of lighting based on rapeseed oil, including a pocket candlestick and an oil lamp with an air-pressurized fuel pump which proved to be very popular.

He then moved on to Kyoto, where he studied rangaku, or western learning, and astronomy. He invented a pneumatic fire pump, and in 1851, he built a myriad year clock which is now designated as an Important Cultural Property by the Japanese government.

With the development of the Sonnō jōi movement, the atmosphere in Kyoto became increasingly dangerous towards foreign influences and technology, and Tanaka was invited by Sano Tsunetami to Saga Domain in Kyūshū, where he was welcomed by Nabeshima Naomasa.

While in Saga, Tanaka designed and built Japan's first domestically made steam locomotive and steam warship. Although he had no previous experience in the field, he had access to a Dutch reference book and had watched the demonstration of a steam engine by the Russian diplomat Yevfimy Putyatin during his visit to Nagasaki in 1853. He later was a student at the Nagasaki Naval Training Center. On its closure and the withdrawal of its Dutch advisors, Tanaka moved back to Saga and worked at the Seirenkata, where he built models of steam warships (both with screws and with side-paddles), a steam locomotive and experimented with making a telegraph and a glass factory.

He was involved in the construction of a reverberatory furnace in Saga for the production of Armstrong guns. In 1864, he returned to his native Kurume Domain, where he assisted in the development of modern weaponry.

In 1873, six years after the Meiji Restoration, Tanaka, then age 74 and still energetic, was invited by the Ministry of Industry to come to Tokyo to make telegraphs at the ministry's small factory. He relocated to the Ginza district in 1875. He rented the second floor of a temple in what is now Roppongi as a workshop that evolved into his first company—Tanaka Seisakusho (Tanaka Engineering Works), the first manufacturer of telegraph equipment in Japan. After his death in 1881, his son founded Tanaka Engineering Works (田中製造所). The company changed its name after Tanaka's death to Shibaura Engineering Works (芝浦製造所) in 1904. After a merger in 1939 with Tokyo Denki it became Tokyo Shibaura Denki, more commonly known today as Toshiba.

title: Tanaka Hisashige


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Talk:1900 Summer Olympics mixed team

I have searced but not found any evidence that Barry T Cooke is a Russian. Google searches for this name and 1900 or words associated with the mixed team and olympics drew no relevant hits. I'm removing the references to nationality. from Cooke. Robertbrockway 07:09 Apr 26, 2005 (UTC)

I think this article might be more informative if it covered the subject of mixed teams at the Olympics more generally, rather than just the 1900 games. I looked at the linked web site and it appears that mixed teams only appeared in the 1896, 1900, and 1904 games, but I didn't go further ahead than 1920. (Just edit the year in the URL after you get to the page.) Does anyone know if they were banned after 1904, or if they just died out, or if there actually were later instances? It appears there was a combined US/Cuban fencing team in 1904, which must have been pretty interesting. (Update: I just checked up to 1948, and can find no mixed teams post 1904.) --DavidConrad 04:52, 31 August 2005 (UTC)
 * Before 1908 national delegations were not officially recognized, and athletes participated as individuals. That allowed for teams of mixed nationalities. From 1908 onward athletes were only entered by their national Olympic commitee, and mixed teams were no longer possible.

--Nitsansh 21:55, 1 March 2006 (UTC)

title: Talk:1900 Summer Olympics mixed team


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Wikipedia:Featured article candidates/San Francisco-Oakland Bay Bridge/Archive1

San Francisco-Oakland Bay Bridge
This is the best article I've seen about a bridge, tunnel or road. -- Samuel Wantman 07:11, 26 Apr 2005 (UTC)

 * Object. While it is a good article in many ways, it is too unstable and too weighted towards current events.  Much of the content - somewhere around half - is dedicated to events surrounding the current construction of the Eastern span of the bridge, which are really only momentarily relevant.  As an encyclopedia article, I think that such information should really be put into historical context, in which case it should really just be given a small section at most.  Nothing that is going on with the Eastern span is of more significance than, say, the events going on at the time of the bridge's initial construction.  Additionally, since half of the bridge is about to be replaced, it is about to become a dramatically different bridge.  Much of the current article is going to be out-of-date within a year or two, which makes it ineligible, at least in my interpretation of the "stable" requirement. Jun-Dai 07:27, 26 Apr 2005 (UTC)
 * A separate article can and should concentrate on the details of the current reconstruction as well as having an appropriately-sized amount of text in this article that summarizes the most important points about the current reconstruction. --mav 16:11, 26 Apr 2005 (UTC)

 * Question about the configuration: It appears from bus schedules that buses go betwen the Transbay Terminal and the bridge. But there is only a connection to the lower level of the bridge. How do inbound buses get to the terminal? --SPUI (talk) 07:41, 26 Apr 2005 (UTC)
 * see "http://maps.google.com/maps?ll=37.788602,-122.392856&spn=0.009601,0.009938&t=k&hl=en" - the ramps into and out of the terminal (the loop) are transit only, note the connection with the outbound off ramp that runs parallel to the one with the automobiles (not shown in the map, but present in the satellite image. Leonard G. 8 July 2005 02:16 (UTC)

 * I agree with User:Jun-Dai. The focus on recent modifications of the bridge is too great. Phils 16:11, 26 Apr 2005 (UTC)

 * Many of the reasons for objecting above are ironicly what I like about this article and why I chose to nominate it. Wikipedia, by its very nature is able to do things that traditional encyclopedias could only dream about, and one of them is to be extremely current.  We can have articles that are up to date AND encyclopedic.  Think about it, many people more than normal are likely to look up this article because it is a timely subject.  What is being faulted should be held up as an example of what is possible with this media.  -- Samuel Wantman 18:59, 26 Apr 2005 (UTC)
 * I disagree. I think that focus on the current popular consciousness of a subject should be the aim of a separate wiki.  I think it is good that we can have up-to-date information on current events, but this should never be used as the focus of an article that is not a current event, and current events should (IMO) never be featured.  Reconstruction of the Eastern span of the San Francisco-Oakland Bay Bridge (or some more suitable title) ought to have up-to-date information on the current ongoings of that project, and over time it should develop a historical perspective.  The article we are discussing, however, is not a current event (even though current events are going on related to it), and it should not be focussed on what is happening now--such things only need a mention and, where someone is willing to supply the details, a separate entry. Jun-Dai 19:36, 26 Apr 2005 (UTC)

I've implemented the suggestions above. There is now a separate article entitled: Eastern span replacement of the San Francisco-Oakland Bay Bridge --Samuel Wantman 08:00, 6 May 2005 (UTC)

I also pulled out the weld controversy details from the replacement article, now in its own sub-sub article.

Think this is close to time to re-submit? Leonard G. 8 July 2005 02:16 (UTC)


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Talk:Cardiac surgery

Wiki Education Foundation-supported course assignment
This article is or was the subject of a Wiki Education Foundation-supported course assignment. Further details are available on the course page. Student editor(s): Ashley oconnell.

Above undated message substituted from Template:Dashboard.wikiedu.org assignment by PrimeBOT (talk) 16:47, 16 January 2022 (UTC)

note
"A 2012 Cochrane systematic review found evidence that..." does not seem to be about a cardiac surgery "technique". Suggest removal or moving paragraph to "history" section. This is not my field, so I am not sure where to move it. Same with next paragraph regarding smoking and cardiac surgery. The "technique" section is lacking in any description of techniques.Jajava (talk) 06:22, 28 November 2013 (UTC)

== What about?

Including something about the roles of the medical team associated with the procedure? The medical and scientific teams, and equipment used and developed for the surgery deserve a mention... Perfusionists, anesthesiologists, anesthetics used, aortic stints, imaging equipment methods and practices.

I'd like to collaborate with anyone interested to include these on the Cardiac surgery page; cheers user:Mattycoze

E. Converse Peirce
I highly doubt the claim Dr. Peirce "paved the way for successful open heart surgery technology in the 1960s and 1970s." Please see my comments in Talk:Membrane oxygenator. The claim may be applicable on the Membrane oxygenator page, but it isn't significant enough to include here. I won't delete the text here yet to get time to substantiate the claim. Dlodge 17:12, 30 December 2006 (UTC)
 * No response. Removed text. Dlodge 20:29, 4 January 2007 (UTC)

Claims re: Daniel Hale Williams
The claims regarding Daniel Hale Williams performing the first open heart surgery are incorrect for a variety of reasons:
 * Dr. Williams was not the first to repair a pericardial wound - Henry Dalton sutured a pericardium in 1891. Dr. Williams did in fact repair the pericardium of James Cornish in 1893, who had been stabbed in the chest. Surgery within the chest was unheard of in those days due to the almost inevitable infection and resulting death.
 * The pericardium is not part of the heart - it is the sac surrounding the heart. Dr. Williams did not suture the heart, so in fact he did not perform any type of surgery on the heart.
 * "Open heart surgery" is a widely overused term. Coronary artery bypass surgery is not in fact "open-heart" - the bypass grafts are sewn onto the outside of the heart.  True open heart surgery entails things such as valve replacement when the heart is cut open and surgery is performed inside the heart.

For the above reasons, I have removed the claims regarding Dr. Williams. The Wikipedia page on Dr. Williams gives a good description (with references) of his surgery on the pericardium. Dlodge 05:57, 28 January 2007 (UTC)

The term "Open heart surgery" refers to the use of extracorporeal circulation during the operation, which means stopping the heart and relying on a heart-lung machine, regardless of whether the heart chambers are cut open or not. So, a coronary bypass operation is an open procedure if done under extracorporeal circulation, even if the heart chambers need not be opened. —Preceding unsigned comment added by 78.187.37.182 (talk) 14:38, 9 November 2008 (UTC)

I don't think this last comment makes sense unless surgeons have decided to mangle the English language! Surely the words "open" and "heart" have a plain meaning? They mean the heart has been cut open for a surgical procedure. Extra corporeal circulation was not used originally but is a very desirable refinement of open heart surgery that was introduced early on. A coronary bypass clearly involves "cutting" the heart. Whether you treat that as "opening" is a semantic and technical question which I am not qualified to judge but "extracorporeal circulation" ought not to be the criterion for the use of this plain and simple term "open heart". If a term were needed then "suspended heart" would be better. Budhen (talk) 15:21, 31 January 2009 (UTC)

Dlodge & Budhen: Although your proposed definition of "open heart surgery" may have merit, Wikipedia should reflect standard usage, which is along the lines of the preceding comment, i.e. "surgery in which the heart is exposed and the blood made to bypass it". This usage is documented by the following online dictionaries: www.nlm.nih.gov/medlineplus, www.healthline.com/health, www.medicinenet.com, cardiac.surgery.ucsf.edu, www.thefreedictionary.com, medical-dictionary.thefreedictionary.com, www.healthgrades.com. For more references, try googling ":define open heart surgery" (without the quotation marks). Nasorenga (talk) 17:56, 25 February 2015 (UTC)

www.heart-valve-surgery.com
http://meta.wikimedia.org/wiki/Talk:Spam_blacklist#heart-valve-surgery.com

According to the above link to the spam blacklist, this site is merely an advertisement... Per policy, it's been deleted.

So please, quit adding it back in.

60.234.236.149 07:07, 26 March 2007 (UTC)

Nazih Zuhdi
I trimmed the WP:Coatrack on Nazih Zuhdi to what was referenced and seemed relevant to this article. He may be worth his own article though. The extra information can be found at this diff AIR corn (talk) 06:22, 24 May 2011 (UTC)

No mention of Blalock-Taussig Shunt
Why is there no mention of the work of Alfred Blalock, Helen Taussig and Vivien Thomas at Johns Hopkins University? It seems their work predates the work of Sellors and Brock mentioned in the article. — Preceding unsigned comment added by 1lucky2 (talk • contribs) 20:21, 8 April 2012 (UTC)

No mention of Dr. Favaloro
Why not mention it to Dr. René Favaloro, who was the founder of the bypass and eminence of cardiac surgery? — Preceding unsigned comment added by 181.46.95.180 (talk) 02:01, 29 June 2013 (UTC)

TEVAR
At the moment, I've created a redirect from TEVAR to the page for Endovascular aneurysm repair, which I think is OK for the time-being. I know some cardiac surgeons who would want to at least list TEVAR on the template for cardiac surgery procedures.

Since TEVAR is performed by both cardiac and vascular surgeons, perhaps someone who works on CT surgery stuff can work with me on this? Thanks. Bakerstmd (talk) 21:52, 25 March 2014 (UTC)

Kidneys
... sometimes struggle after cardiac surgery, and this may contribute to mortality. Review: 10.2215/CJN.07830814 JFW | T@lk  10:27, 9 March 2015 (UTC)

Open Heart Surgery Under Local Anesthesia?!
In the first paragraph of the article section titled "Open Heart Surgery" we read that in 1953 "Soviet surgeon Aleksandr Aleksandrovich Vishnevskiy conducted the first cardiac surgery under local anesthesia. During this surgery, the heart is exposed and the patient's blood is made to bypass it." No citation is given to support this claim of heart surgery under local anesthesia in either this article, nor in the brief article on Dr. Vishnevskiy. Open heart surgery performed under local anesthesia - where the patient is awake and conscious - seems highly implausible. An article from the JAMA found at this website: http://jama.jamanetwork.com/article.aspx?articleid=1104440  states that open heart surgery requires general anesthesia. If the statement about the 1953 Soviet surgeon is true, then it needs to be elaborated upon and hopefully supported with a citation or two. But as it stands now, it looks to be either an error confusing "general" with "local" or a joke. Qdiderot (talk) 23:45, 5 April 2015 (UTC)

I am planning to contribute in this page. I am hoping to add more information about bypass. Celena21 (talk) 21:48, 29 April 2015 (UTC) User:Celena21/Open heart surgery

I am planning to add to this page discussing what happens after surgery along with details involving heart transplants using the following resources: Ashley oconnell (talk) 17:29, 22 February 2016 (UTC)Ashley O'Connell

Heart Transplants and Post-Surgical Care
Diving into cardiac surgery there are many kinds of surgeries that one can discuss and aside from that, there are many reasons why a patient may receive a cardiac surgery. Aside from the many types of cardiac surgeries that occur, one surgery that is the most visual in the field is open-heart surgery. Open-heart surgery is when there is about an 8-inch incision that a patient receives over their chest and then the surgeon continues with the procedure and follows it with closing the incision. A common open-heart surgery procedure is one that is very complex and strategically thought out prior to, and that is a heart transplant. Heart transplants are not necessarily common but a procedure that is obviously completed while the chest cavity is completely exposed. Heart transplants occur when a patient has a portion or portions of their heart that are not working properly and are unable to be healed on their own. A heart transplant is a very intense operation and common complications that can occur involve rejection of the heart. Meaning the person receiving the donor heart rejects the organ. If the patient who is receiving a heart surgery accepts the heart, it is a very successful surgery and few complications occur when the right steps are completed following the procedure. Following an open-heart procedure, along with many other surgical procedures, there are certain steps that a patient needs to take post-operation. Incision care is very important to not only heal the scar that occurred from the surgery in the best way possible, but also to avoid getting any infections that could occur if the incision is not cleaned properly. Aside from taking care of the incisions and scarring that is present, it is important to understand that you body is still getting accustomed to something new therefore other side effects may occur. Not having an appetite along with swelling can be common side effects to any surgery therefore it is beneficial to expect these changes when approaching a surgery as serious as open-heart surgery. Ashley oconnell (talk) 04:39, 1 March 2016 (UTC)Ashley O'Connell

Peer Review
Hi Ashley,

You certainly picked a difficult task for your article! But it is also an accomplishment for your efforts!

I was not quite sure based on your discussion forum post. Are you adding your paragraph to the current lead section? OR replacing them all? I think the lead section should serve as the purpose of briefing all the potential related topics, defining the scope of the article and offering a broad definition to the topic. There are rooms to improve in this regards. I think the current version of the article has a clear structure. 1	Etymology 2	Agent, host range, symptoms, impact 3	History 4	Infection 5	Disease progression 5.1	Gastrointestinal and respiratory signs 5.2	Neurological signs 5.3	Lasting signs 6	Diagnosis 7	Prevention 8	Treatment 9	Relation to Paget's disease 10	Prevalence 10.1	Contributing factors 11	Further reading 12	References 13	External links

I would suggest you to move Etymology and Agent, host range, symptoms, impact all to under History. The rest of topics are in the order of a reader's expectations.

Again, I was not quite sure where do you plan to put your article in the current version. Just by reading your paragraph, I think it might be a good way for lead section instead of the body part of the article. But as a body part of a WikiPedia article, it lacks depth and details to be informative.

I hope you enjoy working on your article and good luck! Haitaoyu (talk) 22:43, 4 April 2016 (UTC)

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Talk:Donald Richie

Homosexuality
Since this is a Living person, I don't want to make a libelous addition of Category:LGBT people from the United States and Category:LGBT writers, but this article clearly mentions "his homosexuality." Does anyone have a citation from Richie himself? Heroeswithmetaphors (talk) 13:10, 25 April 2010 (UTC)
 * Also this blog calls him "the gay Lafcadio Hearn," but we still need a real source. Can somebody please cite The Japan Journals: 1947-2004? Heroeswithmetaphors (talk) 14:53, 25 April 2010 (UTC)
 * Richie writes of his homosexuality in Japan Journals though he by no means considers himself a "gay writer." In fact, Richie dislikes labels and the idea of "belonging to groups", whether the group be "Americans," "homosexuals," whatever...I suggest you begin with Japan Journals.  Also, I believe a review of Japan Journals in the New York Review of Books by Ian Buruma mentions Richie's homosexuality...Gobledeegooke (talk) 03:33, 5 March 2011 (UTC)

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title: Talk:Donald Richie


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Talk:Boy (I Need You)

Comments
This article needs to be rewritten to tone down the POV language. And is this original work? RickK 07:16, Apr 26, 2005 (UTC)
 * I'm not seeing the POV you speak of. Could you cite an example? Otherwise I think we should remove the template. Everyking 19:10, 27 Apr 2005 (UTC)
 * How about The lyrics of the song were also largely criticized by fans although it should be noted that many radio critics also felt that the lyrics of this song were less ditzy than bigger hits, such as "Heartbreaker", "Dreamlover", "Fantasy", and "It's Like That".

The music video, one of Mariah's most bombastic and complex? RickK 22:06, Apr 27, 2005 (UTC)

Perhaps that could be toned down slightly. But I think citing it would work just as well. Everyking 22:15, 27 Apr 2005 (UTC)

 * "bombastic" is clearly POV, and the radio critics' opinion is not supported. RickK 04:18, Apr 28, 2005 (UTC)

What does until the fans hoarded Mariah mean? I wanted to fix it, by I have no idea what to fix it to. RickK 19:06, Apr 28, 2005 (UTC)

“The One”
Shouldn't "The One" have its own page between "Through The Rain" and "Boy (I Need You)"?

If "Underneath the Stars," "Whenever You Call," "Sweetheart," "Do You Know Where You're Going To (Theme From Mahogany)," and "Last Night a DJ Saved My Life" have their own pages although the singles were either unreleased or withdrawn, then "The One" should have a page of its own, too. Promotional CDs were pressed, club mixes were commissioned and leaked to DJs and webmasters, and a hip-hop remix was produced and recorded. The music video that became "Boy (I Need You)" was originally shot in Japan as the video for "The One."

 * Fair enough. OmegaWikipedia 18:46, 16 August 2005 (UTC)

Merge into "Boy (I Need You)
The songs "You Got Me" and "Irresistible (Westside Connection)", cannot necessarily be considered "singles" if the vinyl release, "MC...Move the Crowd", was used as a "tester". It would than constitute as as an album sampler, like the album samplers released for Mariah Carey and Glitter. Thus, I think that the relevant info in these articles should simply be merged into the "Boy (I Need You)", as it was the only song on the sampler that actually transformed into a single. In addition, the information featured in the articles are either redundant, unnecesary, cruft, or can be found elsewhere. Any relevant info on song production and credentials can simply be put into the Charmbracelet album article. —The preceding unsigned comment was added by Grey Pursuit (talk • contribs) 03:51, 12 March 2006.

List of remixes removed
I've enclosed the list of remixes in hidden comments because not all of them can be notable enough to mention in the article. Here's the list for those who know which of these are notable. Extraordinary Machine 18:32, 25 November 2006 (UTC)

The Remixes A Cappella ft. Cam'Ron 3:58 Agent X 4x4 Instrumental 5:47 Agent X 4x4 Vocal Mix 6:30 Agent X Dutti Boy Instrumental 5:15 Agent X Dutti Boy Mix 5:18 Album Version Ft. Cam'Ron 5:15 Copenhaniacs Remix Ft. Cam'Ron 4:37 Instrumental 5:02 Just Blaze Remix Extended 5:13 Just Blaze Remix 3:52 Panjabi Hit Squad Mix Ft. Cam'Ron 4:16 Radio Edit - Ft. Cam'Ron 4:01 Radio Edit - Instrumental 4:01 Radio Edit/No Rap 3:16 Remix by The Duke & MVP from Disco Montego Ft. Cam'Ron 4:04 Street Remix Ft. Cam'Ron, Juelz Santana, Jimmy Jones & Freeway 5:32 Street Remix Radio Edit Ft. Cam'Ron, Juelz Santana, Jimmy Jones & Freeway 4:01 Street Remix Instrumental 5:32 Topnotch L8 Mix 4:14 Topnotch Tox Mix 4:17 Vice Remix 4:23

source: www.mcarchives.com

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text: Talk:Eviction

title: Talk:Eviction


text:
Add-drop multiplexer

An add-drop multiplexer (ADM) is an important element of an optical fiber network. A multiplexer combines, or multiplexes, several lower-bandwidth streams of data into a single beam of light. An add-drop multiplexer also has the capability to add one or more lower-bandwidth signals to an existing high-bandwidth data stream, and at the same time can extract or drop other low-bandwidth signals, removing them from the stream and redirecting them to some other network path. This is used as a local "on-ramp" and "off-ramp" to the high-speed network.

ADMs can be used both in long-haul core networks and in shorter-distance "metro" networks, although the former are much more expensive due to the difficulty of scaling the technology to the high data rates and dense wavelength division multiplexing (DWDM) used for long-haul communications. The main optical filtering technology used in add-drop multiplexers is the Fabry–Pérot etalon.

Newer "multi-service SONET/SDH" (also known as a multi-service provisioning platform or MSPP) equipment has all the capabilities of legacy ADMs, but can also include cross-connect functionality to manage multiple fiber rings in a single chassis. These devices can replace multiple legacy ADMs and also allow connections directly from Ethernet LANs to a service provider's optical backbone. At the end of 2003, sales of multiservice ADMs exceeded those of legacy ADMs for the first time, as the change to next-generation SONET/SDH networks accelerated.

An emerging variety of ADMs that is becoming popular as the carriers continue to invest in metro optical networks are reconfigurable optical add-drop multiplexers (ROADMs).

title: Add-drop multiplexer


text:
Talk:Steelpan

Pannists
Some key pannists are missing from the list: Rudy Smith Robert Greenidge Earl Rodney Ken "Professor" Philmore Annise Hadeed Ron Reid Garvin Blake Nkr8 (talk) 15:20, 5 December 2021 (UTC)

"contexts other than those with which it is stereotypically associated"
This section is written from a white gaze and assumes that the things that matter are the things that happen outside of TT. Statements like The first known use of steelband in a theatrical performance (outside of Trinidad and Tobago) make this very clear. It's pretty much a collection of "the first white people to do x with pan" anecdotes. As things stand in the article, I don't think this belongs. Guettarda (talk) 00:18, 23 January 2022 (UTC)

title: Talk:Steelpan


text:
Split pin

A split pin, also known in the US as a cotter pin or cotter key, is a metal fastener with two tines that are bent during installation, similar to a staple or rivet. Typically made of thick wire with a half-circular cross section, split pins come in multiple sizes and types.

The British definition of "cotter pin" is equivalent to US term "cotter". To avoid confusion, the term split cotter is sometimes used for a split pin. A further use of the term "cotter pin" is the "crank cotter pin" used to lock bicycle pedal cranks to the bottom bracket axle. These are not "split" at all and are wedge shaped.

Construction

A new split pin (see figure A) has its flat inner surfaces touching for most of its length so that it appears to be a split cylinder (figure D). Once inserted, the two ends of the pin are bent apart, locking it in place (figure B). When they are removed they are supposed to be discarded and replaced, because of fatigue from bending.

Split pins are typically made of soft metal, making them easy to install and remove, but also making it inadvisable to use them to resist strong shear forces. Common materials include mild steel, brass, bronze, stainless steel, and aluminium.

Types

The most common type of split pin is the extended prong with a square cut, but extended prongs are available with all of the other types of ends. The extended prong type is popular because the difference in length of the two tines makes it easier to separate them. To ease insertion into a hole the longer tine may be slightly curved to overlap the tip of the shorter tine or it is beveled.

Hammer lock split pins are properly installed by striking the head with a hammer to secure the pin. This forces the shorter tine forward, spreading the pin.

Types include standard, humped and clinch.

Sizes
The diameters of split pins are standardized.

American split pins start at $1/32$ in and end at $3/4$ in. Metric conversions in the table below are approximate.

Applications

Split pins are frequently used to secure other fasteners, e.g. clevis pins, or to secure a castellated nut, or, infrequently, as a low-tech shear pin.

Split pins are cheaper but less reusable than linchpins, and provide less strength but easier to install/remove than spring pins.

title: Split pin


text:
Talk:Population density

Vandals
This page seems to get alot of vandals messing it up. When you restore pages please make sure you are restoring to the last "good" page not removing "bad" words because some of the vandals seem to like delete paragraphs out of the page. (I know it is redundant to say this but sometimes it hasnt been done ) --2mcm 07:21, 26 Apr 2005 (UTC)

 * Why does this page get so many vandals ? --2mcm 05:43, 11 May 2005 (UTC)

 * Maybe it's those people over at overpopulationisamyth.com ;)  Impfireball (talk) 07:09, 31 August 2015 (UTC)

Alternative more detailed map
I have seen a map showing world population density in detail in Wikipedia, which is more useful than density on a population basis in my opinion, as eg it shows the density of Java and the massive block of ultra density in China, neither of which is apparent here. Unfortunately I can't remember where I saw it. If anyone can find it, please add it here. Sumahoy — Preceding undated comment added 15:12, 2 June 2006 (UTC)

 * I found it and added it, but unfortunately it is based on 12 year old data. —Preceding unsigned comment added by Sumahoy (talk • contribs) 15:27, 2 June 2006

 * The map is pretty uninformative, it just shows the average density for an entire country, I first noticed when Alaska was the same colour as the mainland USA, some countries vary greatly, whereas others like hong kong or India are generally very densly populated, the map should reflect this —Preceding unsigned comment added by 81.154.25.187 (talk • contribs) 18:07, 18 September 2006

 * I really think that we need a newer map here - 1994 is a little outdated. Moreover, that map doesn't represent Russia very accurately at all, and completely misses several major cities.  If a better version of that map is found, it should be placed at the top of the article instead of in a section - after all, we already have an article called "countries by population density", with that countries map at the top.  I think that the density/square km map is much more useful and explains the concept of population density better. Esn 09:22, 11 November 2006 (UTC)

 * I agree. Average density for an entire country, colored by political boundaries, is misleading and of limited usefulness.  For instance Alaska abuts Canada and looks more densely populated, because it's part of the USA and is figured in with the USA population density.  The second map is much more accurate, but 1994 is very out of date--more than a billion have been added since that map.  Also, the color scale is not too great; for a highly clustered factor like population, a logarithmic color scheme would be much better.  As is, it is impossible to distinguish between population density among the less populous areas.  Unfortunately accurate global data is difficult to get and making such a map is not trivial. NTK (talk) 09:19, 9 December 2007 (UTC)

 * The maps don't match up well, they show one of them by cities and one by countrys. Perhaps delete 1994 one until better map found? —Preceding unsigned comment added by 24.62.108.94 (talk) 02:09, 25 December 2008 (UTC)

 * see Talk:Choropleth_map —Preceding unsigned comment added by 71.167.60.30 (talk) 01:01, 10 August 2009 (UTC)

 * 1994 map is useful if old but note that borders do not represent political landscape of 1994, see especially yugoslavia and czechoslovakia are still united. — Preceding unsigned comment added by 67.164.148.14 (talk) 18:20, 21 February 2015 (UTC)

Density ranges
If anyone has a source to find it, it'd be great to add a set of typical density ranges for various settlement types: urban, suburban, rural, etc. Readers, like myself, may come to this page looking to get a sense of roughly how dense a particular value is. -Will Beback · † · 08:53, 23 November 2006 (UTC)

Least densely populated place
This article mentions Mongolia as the least densely populated country in the world, but I thought Greenland was. They both register as below 0/km². — Preceding unsigned comment added by 81.79.156.215 (talk) 20:15, 12 June 2007 (UTC)

 * Greenland is less densely populated, but it is not strictly a "country" but a self-governing territory of Denmark, with the same status as the Faroe Islands. NTK (talk) 09:14, 9 December 2007 (UTC)

 * So why does it say Greenland in the caption, but has a photo of Mongolia? Pick one and be consistent! 24.83.176.234 (talk) 07:08, 11 March 2009 (UTC)

Consequences
I'd like to see a discussion of the consequences of high population density. AThousandYoung (talk) 02:39, 31 May 2008 (UTC)

 * Agreed. I note the article states that excluding Antarctica, the world's population density (including deserts and mountains etc.) is currently 50 per km2. It is fascinating to note that the originally wholly fertile Easter Island's society collapsed when its density reached about 100 per km2.1812ahill (talk) 17:53, 29 November 2011 (UTC)

 * Yes, that should be mentioned, if not already. Impfireball (talk) 07:08, 31 August 2015 (UTC)

population density
THIS IS VERY HARD STUFF TO FIGURE OUT PEOPLES. HOW DO YOU OLD PEOPLE DO IT. IT'S SO HARD. AND HOW THE HELL ARE YOU SUPPOSED TO FIGURE OUT HOW POPULATIO IS MEASURED. —Preceding unsigned comment added by 167.142.168.14 (talk) 21:50, 22 October 2008 (UTC)

 * population density is a simple math formula. Take the total population of a place according to current census data and divide it by the total physical size (land or land and water). For instance, if a place has 1,352,495 square miles and a population of 1519 people, then it has 0.0011 people per square mile (population density) [1519 / 1352495 = 0.0011231095124196392592948587610305], rounded to the nearest ten thousandth. If a place has 50 square miles and 12,853,289 people, then it has 257,065.78 people per square mile [12853289 / 50 = 257065.78], no rounding. hello (talk) 16:54, 1 December 2009 (UTC)

An article in need of some structure and a rewrite!
This article is confused. It needs a big refresh.

It needs:

A definition. The current definition is poor, confusing and inappropriate.

Currently: Population density (in agriculture standing stock and standing crop) is a measurement of population per unit area or unit volume. It is frequently applied to living organisms, and particularly to humans. It is a key term used in geography.

When is it applied to non-living things as opposed to living organisms? Standing crop refers to biomass/energy in a crop not population density - it needs removing. The human part is unnecessary. It is used in both science and social studies/humanities/geography. It has not referred to carrying capacity of the environment or artificially exceeding it (as humans manipulate it for themselves and their livestock and crops).

The Allee effect is not related to fertility but reproductive rates. These are different things. This article seems to be explaining the Allee effect incorrectly. It is also not the place to explain it but explain why the effect is important in population density.

Weasle words about ... considered by some for example, need removing.

Sections referring to other animal and plant populations need adding. These should be before the human population as the human population is a special form of animal population that has artificial carrying capacities.

I question the usefulness and effectiveness of the 1994 world population density map. I believe it should be removed. --Candy (talk) 04:41, 16 January 2009 (UTC)

Populations, land area, and population density
I just compared these figures for several counties of New York. With checking Broome, Chemung, St. Lawrence, Nassau, Tompkins, and Suffolk Counties, I have noticed mistakes in the numbers (not all have mistakes).

I say mistakes. I am not talking about wrong numbers specifically. I am talking about wrong calculation, if any, used. Who ever places the figures either has bad math skills, copies the stuff from inaccurate information elsewhere, or incompletely copies the stuff. The math is pretty easy: Population divided by land (or land and water) area equals population density.

Why are the numbers so far off sometimes? How is the information gathered? How is the information actually put onto the county pages (and those of cities, villages, towns, and hamlets)? hello (talk) 17:18, 1 December 2009 (UTC)

 * This page definitely has bad information on it. On England the population density is listed as 395 people per square kilometer, yet it is not listed in the tables. — Preceding unsigned comment added by 129.101.16.41 (talk) 12:14, 30 April 2012 (UTC)

 * England is not a country. If you use the UK density instead they would not be in the top ten. — Preceding unsigned comment added by 82.27.239.61 (talk) 16:08, 1 September 2012 (UTC)

 * Where is PRC (People's Republic of China) on these lists? It is one of the most densely populated countries, as well as a country with more than 10 million people?  — Preceding unsigned comment added by R10623 (talk • contribs) 05:49, 21 May 2012 (UTC)

Why it's England and not UK
If it was UK we would drop out of the top ten. (And if other regions of countries were included we would drop out of the top ten). It's all politics... 86.2.64.179 (talk) 22:03, 12 September 2012 (UTC)

 * I agree. So I've taken England out. All other countries stated are either sovereign or - in the case of Hong Kong - autonomous. If England is to be included so I suspect ought various US states, Swiss cantons, and other non-sovereign administrative divisions, all of which would have more constitutional autonomy than England which has none. — Preceding unsigned comment added by The Angel of Islington (talk • contribs) 06:54, 29 September 2012 (UTC)

 * That is specious reasoning, England is not comparable to a state of the USA or a Canton of Switzerland, but is comparable to an autonomous or other component region of a country like Gaza Strip, Hong Kong, and Taiwan (and others). England is a political entity, and does posesses some autonomy, as does Wales, Scotland, and Northern Ireland, which by your reasoning would be included. Futhermore, England's population density is concealed by only reporting the UK. England's population density is the highest of any country over 10m people in Europe and in the world; it just misses out of being in the top ten of countries over 1m population. England is restored, because all the other component parts and dependencies of the UK have separate entries. — Preceding unsigned comment added by 212.105.162.130 (talk) 09:56, 2 July 2018 (UTC)

Sri Lanka vs. Japan
These seem to be in wrong order in the table, but I don't know what the mistake has been exactly so I'm not confident to fix it. Also, why on earth is it top nine countries? I'd usually expect ten in such a list, nine just feels random enough to warrant an explanation. — Preceding unsigned comment added by 91.155.240.104 (talk) 10:09, 17 December 2012 (UTC)

Macao
Monaco is 2nd most densely populated country, Macao is 1. --108.92.162.111 (talk) 16:56, 10 March 2013 (UTC)

But why are these areas not on the political list? Especially Monaco is a wholly independent country. 84.202.70.183 (talk) 09:02, 9 August 2014 (UTC)

Picture file has faulty description
The last picture file on this page depicts EU-27, not Europe, as seen by the lack of countries such as Serbia, Croatia, Norway and Iceland. — Preceding unsigned comment added by 2001:700:303:14:B0AF:780E:74F6:B611 (talk) 14:24, 1 April 2014 (UTC)

No mention of Real Estate?
I have no citations, but I have an idea that confronts the one that proposes economic stability is linked to diminishing population growth. The flaw I found was that it assumes that countries like China and India can become further and further economically stable to the point that pop growth actually diminishes to a point of 'stability' (or relatively managable level) like that of a western country.

In my view, this is naive, because I think that there's so many factors that link to economic stability. On one end, there's free trade, which can cause an economy to grow rapidly but also become economically unstable when another country seemingly refuses to rise to stability.

On the other end, there's real estate prices! This seems like a clear observation to me, but I never read about it in any of the article. If the population is high and people are getting richer, real estate development bubbles are created. However, this causes prices to rise rapidly. Eventually, the cost to develop is too high and the economy could actually collapse again, as the cost of living becomes too much. This is effected by high populations, because high demand created at a baseline with a high population (not even including external interested parties, which are very likely to occur when there's a real estate boom), can create major bubbles.

In my view, it is possible for a country to be so populated that it's economy will never stabilize, and it will never develop the infrastructure needed to improve or provide a universal standard of living or one that can accept further populations that aren't made to live in squallor. With overpopulation, growth in standard of living can stagnate, caught in a vortex of rising and lowering, or even recede rapidly.

I think that more research should be done on this issue. Or maybe I'm living in a fantasy land because the "numbers don't lie"? Impfireball (talk) 07:00, 31 August 2015 (UTC)

Population density formula
Good day! I would like to point out that the source used in this article to describe population density does not agree with the text in the article. As it stands now the article reads: Population density is population divided by total land area or water volume, as appropriate. Whereas the source for the this statement reads: To determine an area's population density, you just have to divide an area's total population by the land area in square miles (or square kilometers).   Secondly, the first sentence under the sub-heading Human population density  which reads: ''For humans, population density is the number of people per unit of area, usually quoted per square kilometer or square mile (which may include or exclude, for example, areas of water or glaciers). Commonly this may be calculated for a county, city, country, another territory or the entire world.'' has no source that supports that statement. ——→StephenTS42 (talk) 20:11, 24 May 2017 (UTC)

 * Although I do agree on your second point on how there is no source saying how calculations are commonly used on counties, cities, or countries, I must disagree with your second point. The articles sentence on calculating population density seems to simply be a paraphrase of the source. Both articles are simply saying to divide the population by the area in which they live in. Although I do agree that either a new source that mentions the inclusion of water should be found and used, or to simply exclude the part about using water volume as a divisor while keeping the old source should be done. Tlarican (talk) 21:23, 17 October 2017 (UTC)

Some quality of life changes
As I read through the article, I noticed a few small things that could be changed to make this article more clear and reliable.

As I had mentioned in my reply to StephenTS42's comment, the small sentence on calculating population density is a bit unreliable. Seen directly under the section "Biological population densities," the article states, "Population density is population divided by total land area or water volume, as appropriate." The part that sticks out as unreliable is the water volume part. If I were to calculate the population density of an island and included the water, dividing by the VOLUME of the water would throw my calculations way off. The ocean is a deep thing and by adding the extra layer of the ocean's depth to my calculations would make my population density seem minuscule. The article should probably say "Population density is population divided by total land area or water surface area, as appropriate."

Clarity should also be more apparent in the article. In the sub-section, "Other methods of measurement", the word "other" suggests that the sub-section is going to introduce different methods of calculating population that differ from the one mainly used in the prior sections. However, the prior sections never outright say what the most common way of calculating population density is. The main way of calculating population density, arithmetic density, is only mentioned in this sub-section at the END of the article. The words "arithmetic density" never come up in the main sections of the article. Also, the sentence after at the beginning of the sub-section "Other methods of measurement" mentions arithmetic density and there being more ways of measurement, but then arithmetic density itself appears immediately on the list. This structure is repetitive. Either name the sub-section "Methods of measurement" and keep with the same list, or mention how arithmetic density is the most common way of calculating population density somewhere early in the article and then remove arithmetic density from the list of "other methods of measurement."

In a sort of related track of the last edit, many of the parts of the article require sources. The words "citation needed" are riddled throughout the article, creating a less reliable article. Also, in the sub-section that I had just critiqued about "Other methods of measurement," many of the other methods aren't even sourced. This causes it to seem that these methods have been pulled from thin air. Sources showing who use these methods, such as certain scientists or certain groups of researchers, or how they are used would help bring reliability to that sub-section. Many of the sources are also a bit outdated. Source number seven of the article brings up an article about human population from 2002. In the article, the world's population is mentioned to be only 6 billion. As we know, the population is currently 7 billion and getting close to 8 billion. This sourced article also mentions other articles that are nearing twenty years old.

The last comment I have about the article is a tiny change in wording. In the middle of the sub-section "Human population density" is a sentence that states, "Cities with high population densities are, by some, considered to be overpopulated, though this will depend on factors like quality of housing and infrastructure and access to resources." This "by some" part can be vague. Even if the source were to define who the "some" are, the Wikipedia article should still be precise. Words such as anthropologists, sociologists, or even scientists would create some immediate ethos in the sentence rather than having the reader look through the source to find out who "some" are. Tlarican (talk) 21:23, 17 October 2017 (UTC)

Hemispheres
"In relation to the equator it is seen that the vast majority of the human population lives in the Northern Hemisphere." As opposed to the ocean that dominates the Southern Hemisphere... 84.248.218.89 (talk) 14:46, 22 January 2018 (UTC)

Canada is OBVIOUSLY wrong
How can Canada be dark purple? 35 million people in half the landsize of the USA? Please fix Canada. SystemBuilder (talk) 06:35, 7 October 2021 (UTC)

 * Its not just Canada even, almost everything in the map is wrong, how can Estonia have 2000 per square kilometre, thats just impossible 83.176.189.150 (talk) 17:34, 6 April 2022 (UTC)

2015 Population Density Map by FAO
Maybe this could be useful:

Online map view

Source

--Arthurfragoso (talk) 03:21, 7 March 2022 (UTC)

the population density of the EU map is wrong
The map that uses area and colour to represent population and population density, Lithuania appears to have the Kaliningrad area. — Preceding unsigned comment added by 83.176.189.150 (talk) 17:32, 6 April 2022 (UTC)

Explain the influence of climate on Population and then give other factors for variation using population density terms with examples
Let's start discussion 197.231.239.60 (talk) 20:40, 14 September 2022 (UTC)

Don't be overly accurate
Shouldn't density be expressed in whole numbers? (See Wiki article on "Significant figures"; use only as many as in the least-accurate measurement component.) Carrying out the calculation to a decimal person is illogical — especially considering that the underlying data surely is not accurate even to a basic count only a day or so after a census was taken.Casey (talk) 23:21, 22 January 2023 (UTC)

title: Talk:Population density