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Herman Brood

Hermanus "Herman" Brood  (5 November 1946 – 11 July 2001) was a Dutch musician, painter, actor and poet. As a musician he achieved artistic and commercial success in the 1970s and 1980s, and was called "the greatest and only Dutch rock 'n' roll star". Later in life he started a successful career as a painter.

Known for his hedonistic lifestyle of "sex, drugs and rock 'n' roll", Brood was an enfant terrible and a cultural figure whose suicide by jumping from a hotel roof, apparently influenced by a failure to kick his drug and alcohol habit, strengthened his controversial status; according to a poll organised to celebrate fifty years of Dutch popular music, it was the most significant event in its history.

Musical career
Herman Brood was born in Zwolle, and started playing the piano at age 12. He founded beat band The Moans in 1964, which would later become Long Tall Ernie and the Shakers. Brood was asked to play with Cuby and the Blizzards, but was removed by management when the record company discovered he used drugs. For a number of years Brood was in jail (for dealing LSD), or abroad, and had a number of short-term engagements (with The Studs, the Flash & Dance Band, Vitesse).

In 1976, Brood started his own group, Herman Brood & His Wild Romance (and started work with photographer Anton Corbijn), initially with Ferdi Karmelk (guitar), Gerrit Veen (bass), Peter Walrecht (drums), and Ellen Piebes and Ria Ruiters (vocals). They played the club and bar circuit, first in Groningen (the northeasternmost province of the Netherlands). In 1977 the band released their first album, Street.

The band played all over the Netherlands, playing as many gigs as possible. And Herman's drug habit became public: In 1977 for instance the Wild Romance played a gig in a high school in Almelo, the Christelijk Lyceum; during the break Brood was caught on the toilet taking heroin or speed (there are different reports on the type of drug, but it is a well-known story amongst former students), the rest of the concert was cancelled, and this also was the last time a rock concert took place at this school for many years.

They are still best known for their second album, Shpritsz—a play on the German word Spritze for syringe—from 1978. This album contained Brood anthems like "Dope Sucks," "Rock & Roll Junkie," and their first Dutch hit single, "Saturday Night." The band went through many personnel changes over the years; the best-known formation was Freddy Cavalli (bass), Dany Lademacher (guitar) (later replaced with David Hollestelle), and Cees 'Ani' Meerman (drums). A frequent contributor was Bertus Borgers (saxophone).

Brood's outspoken statements in the press about sex and drug use brought him into the Dutch public arena even more than his music. He was romantically involved with the German singer Nina Hagen, with whom he appeared in the 1979 film Cha-Cha. He is reputed to be the subject of her song "Herrmann Hiess Er" (English title "Herrmann Was His Name") from the 1979 Unbehagen album, a song about a drug addict. Brood relished the media attention and became the most famous hard drug user in the Netherlands. "It is quite common for an artist to use drugs, but not for him to tell everybody. I admit that it scared me that my popularity could make people start using drugs," he once said in an interview.

In the summer of 1979, Brood tried to enter the American market, with support from Ariola's US division, which was attempting to expand into rock music. Following on the success of Shpritsz, the band was booked as a support act for The Kinks and The Cars, playing in auditoriums; "Herman Brood and His Wild Romance Tour Cha Cha '79" headlined in New York's (Bottom Line) and Los Angeles' (Roxy). A re-recorded version of "Saturday Night" peaked at number 35 in the Billboard Hot 100, but the big break Brood hoped for didn't happen. When he returned to the Netherlands in October 1979, his band had begun to fall apart, and soon his popularity went downhill. Go Nutz, the album Brood had recorded while in the States, and the movie Cha-Cha, which finally premiered in December 1979, were considered artistic failures, even though Go Nutz produced three charting singles in the Netherlands and the Cha Cha soundtrack attained platinum status. The 1980 album Wait a Minute... was a minor success, but the follow-up albums Modern Times Revive (1981) and Frisz & Sympatisz (1982) failed to make the Dutch album charts.

Brood continued to record throughout the 1980s and had a few hits—a top-10 single, "Als Je Wint" with Henny Vrienten, and a minor hit with a reggae song, "Tattoo Song," but he spent more and more time on his art work. At the end of the '80s he made a comeback of sorts; Yada Yada (1988), produced by George Kooymans, was well-received, and he toured Germany with a renewed Wild Romance (which saw the return of Dany Lademacher). In 1990, he won the BV Popprijs, one of the highest Dutch awards for popular music, and recorded Freeze with Clarence Clemons of the E Street Band and Tejano accordion player Flaco Jiménez. A live "best of" album, Saturday Night Live, appeared in 1992. His 50th birthday, in 1996, was celebrated with a show at the Paradiso music and cultural center in Amsterdam, and the album (of duets) was released the same year.

Visual arts career
After his career in music, Brood turned to painting and became a well-known character in Amsterdam art circles. His art is best described as pop-art, often very colorful and graffiti-inspired screen prints, and he achieved some commercial success and notoriety by, for instance, creating murals in various public spaces in and around Amsterdam. He continued to remain in the public eye, by appearing in the media and by his cooperation with biographical films such as 1994's Rock'n Roll Junkie.

Suicide and legacy
Toward the end of his life, Brood vowed to abstain from most drugs, reducing his drug use to alcohol and a daily shot of speed ("2 grams per day" ). On 11 July 2001, depressed by the failure of his drug rehabilitation program and facing serious medical problems because of his prolonged drug use, he committed suicide by jumping from the roof of the Amsterdam Hilton Hotel at the age of 54. He left a note, stating "Ik heb er geen zin meer in, misschien zie ik jullie nog wel eens. Maak er een mooi feest van." which translates to "I don't feel like it anymore, maybe I'll see you all again some day. Have a nice party." Extensively covered by the national media, his cremation took place five days later. Before the cremation, Brood's coffin was driven from the Hilton hotel to Paradiso, Amsterdam, the streets lined with thousands of spectators. A commemorative concert was held in Paradiso, with performances by Hans Dulfer, André Hazes, and Jules Deelder, and the leading Dutch music magazine Muziekkrant OOR devoted an entire issue to him. His ashes were inurned at Zorgvlied cemetery.

Soon after his suicide, Brood's version of "My Way" spent three weeks as number one in the Dutch singles charts; the market value of his art work also increased greatly. A characteristic note is that Brood's paintings had often been targeted by vandals during his life, but after his death they were stolen for their value. His popularity (or notoriety) was confirmed by the fact that his name turned out to be the strongest brand of the year.

When U2 performed in the Netherlands three weeks after Brood's suicide, they paid tribute to him at each of the three shows. They dedicated a version of "Stuck in a Moment You Can't Get Out Of" (written for Michael Hutchence after his death) to him, with Bono singing Brood's "When I Get Home" as an a capella intro.

At the third show in Arnhem they also dedicated their own "Gone" to him and had his version of "My Way" played over the PA as outro music. In the middle of the show Bono delivered an emotional eulogy to Brood before the band performed "In a Little While".

On 5 November 2006 the Groninger Museum opened an exposition devoted to Herman Brood's life and work, comprising paintings, lyrics, and poetry, portraits by photographer Anton Corbijn, a collection of private pictures (from the family album), and concert photos and videos. The exhibition continued until 28January. It was centered on Herman's atelier (studio) where he created most of his paintings. The atelier had been entirely re-built in the museum. During the 1990s, Herman Brood's studio was located on the second floor of the gallery in the Spuistraat in Amsterdam and has remained untouched since his death.

In 2007 the film Wild Romance, a movie about Brood's life, premiered in the Netherlands, with Brood portrayed by Daniël Boissevain. He continues to inspire other artists: the 2007 album Bluefinger by Black Francis is based on Brood's life and works. A tribute band called the Brood Roosters ("bread toasters") was active in the Netherlands until they split up in early 2009. Another tribute band called Yada Yada is still active in the Netherlands, often appearing with original members of the Wild Romance (Dany Lademacher, Ramon Rambeaux).

In 2010 the Catastrophic Theatre Company collaborated with Frank Black on a rock opera based on the Bluefinger album. The opera's first performance, with Matt Kelly portraying Brood, was on 12 November 2010 in Houston, Texas.

Discography (albums)

 * Street (1977)
 * Shpritsz (1978)
 * Cha Cha (1978)
 * Cha Cha (1979, soundtrack for the movie Cha Cha)
 * Herman Brood & His Wild Romance (1979, Shpritsz re-release for US market, contains an edited version of Saturday Night)
 * Go Nutz (1980)
 * Wait a Minute... (1980)
 * Modern Times Revive (1981)
 * Frisz & Sympatisz (1982)
 * The Brood (1984)
 * Bühnensucht (1985, live album)
 * Yada Yada (1988)
 * Hooks (1989)
 * Freeze (1990)
 * Saturday Night Live! (1992)
 * Fresh Poison (1994)
 * 50 – The Soundtrack (1996 duets, a tribute album for his 50th birthday)
 * Back on the Corner (1999)
 * Ciao Monkey (2000)
 * My Way – The Hits (2001)
 * Final (2006, 3-CD compilation)

Filmography

 * Cha-Cha (1979)
 * Stadtrand (1987, German movie)
 * Zusje (1995) - Bovenbuurman / Upstairs neighbor
 * Total Love (2000, Israeli movie) - M.J
 * Rock 'N Roll Junkie (1994, documentary)
 * Live And More (2003, Concerts from Philipshalle, Düsseldorf 1978 & Musik Hall, Koln 1990 (3DVDBox))
 * Wild Romance (2006, scenes from Herman Brood's life)
 * Herman Brood Uncut (2006, documentary)
 * Kunst begin drrr niet an (2015, 80 min. documentary by Gwen Jansen, DVD, 90% of all screenprints and paintings are made by Herman in the IQ studio between the late 80s until his passing in 2001. Compiled from over 70 hours of footage, produced by Ivo de Lange for iq.nl)
 * Unknown Brood (2016, documentary directed by Dennis Alink)

Literature

 * Book and DVD.
 * Brigitte Tast, Hans-Juergen Tast (2009) "be bop" – Rock-Tempel & Nachtasyl – Band 2 zur Legende. Hildesheim: Verlag Gebr. Gerstenberg. ISBN 978-3-8067-8733-7.
 * Brigitte Tast, Hans-Jürgen Tast (2016) Herman Brood. Der Ladykiller im "be bop", Schellerten 2015, ISBN 978-3-88842-049-8.
 * Brigitte Tast, Hans-Juergen Tast (2009) "be bop" – Rock-Tempel & Nachtasyl – Band 2 zur Legende. Hildesheim: Verlag Gebr. Gerstenberg. ISBN 978-3-8067-8733-7.
 * Brigitte Tast, Hans-Jürgen Tast (2016) Herman Brood. Der Ladykiller im "be bop", Schellerten 2015, ISBN 978-3-88842-049-8.
 * Brigitte Tast, Hans-Jürgen Tast (2016) Herman Brood. Der Ladykiller im "be bop", Schellerten 2015, ISBN 978-3-88842-049-8.

title: Herman Brood


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Homomorphism

In algebra, a homomorphism is a structure-preserving map between two algebraic structures of the same type (such as two groups, two rings, or two vector spaces). The word homomorphism comes from the Ancient Greek language:  meaning "same" and   meaning "form" or "shape". However, the word was apparently introduced to mathematics due to a (mis)translation of German meaning "similar" to ὁμός meaning "same". The term "homomorphism" appeared as early as 1892, when it was attributed to the German mathematician Felix Klein (1849–1925). See:
 * From footnote on p. 22: "Ich will nach einem Vorschlage von Hrn. Prof. Klein statt der umständlichen und nicht immer ausreichenden Bezeichnungen:  "holoedrisch, bezw. hemiedrisch u.s.w. isomorph" die Benennung "isomorph" auf den Fall des holoedrischen Isomorphismus zweier Gruppen einschränken, sonst aber von "Homomorphismus" sprechen, … " (Following a suggestion of Prof. Klein, instead of the cumbersome and not always satisfactory designations "holohedric, or hemihedric, etc. isomorphic", I will limit the denomination "isomorphic" to the case of a holohedric isomorphism of two groups; otherwise, however, [I will] speak of a "homomorphism", … )
 * From p. 466: "Hierdurch ist, wie man sofort überblickt, eine homomorphe*) Beziehung der Gruppe Γ(63) auf die Gruppe der mod. n incongruenten Substitutionen mit rationalen ganzen Coefficienten der Determinante 1 begründet." (Thus, as one immediately sees, a homomorphic relation of the group Γ(63) is based on the group of modulo n incongruent substitutions with rational whole coefficients of the determinant 1.)  From footnote on p. 466:  "*) Im Anschluss an einen von Hrn. Klein bei seinen neueren Vorlesungen eingeführten Brauch schreibe ich an Stelle der bisherigen Bezeichnung "meroedrischer Isomorphismus" die sinngemässere "Homomorphismus"."  (Following a usage that has been introduced by Mr. Klein during his more recent lectures, I write in place of the earlier designation "merohedral isomorphism" the more logical "homomorphism".)

Homomorphisms of vector spaces are also called linear maps, and their study is the subject of linear algebra.

The concept of homomorphism has been generalized, under the name of morphism, to many other structures that either do not have an underlying set, or are not algebraic. This generalization is the starting point of category theory.

A homomorphism may also be an isomorphism, an endomorphism, an automorphism, etc. (see below). Each of those can be defined in a way that may be generalized to any class of morphisms.

Definition
A homomorphism is a map between two algebraic structures of the same type (that is of the same name), that preserves the operations of the structures. This means a map $$f: A \to B$$ between two sets $$A$$, $$B$$ equipped with the same structure such that, if $$\cdot$$ is an operation of the structure (supposed here, for simplification, to be a binary operation), then
 * $$f(x\cdot y)=f(x)\cdot f(y)$$

for every pair $$x$$, $$y$$ of elements of $$A$$. One says often that $$f$$ preserves the operation or is compatible with the operation.

Formally, a map $$f: A\to B$$ preserves an operation $$\mu$$ of arity $$k$$, defined on both $$A$$ and $$B$$ if
 * $$f(\mu_A(a_1, \ldots, a_k)) = \mu_B(f(a_1), \ldots, f(a_k)),$$

for all elements $$a_1, ..., a_k$$ in $$A$$.

The operations that must be preserved by a homomorphism include 0-ary operations, that is the constants. In particular, when an identity element is required by the type of structure, the identity element of the first structure must be mapped to the corresponding identity element of the second structure.

For example:

 * A semigroup homomorphism is a map between semigroups that preserves the semigroup operation.
 * A monoid homomorphism is a map between monoids that preserves the monoid operation and maps the identity element of the first monoid to that of the second monoid (the identity element is a 0-ary operation).
 * A group homomorphism is a map between groups that preserves the group operation. This implies that the group homomorphism maps the identity element of the first group to the identity element of the second group, and maps the inverse of an element of the first group to the inverse of the image of this element. Thus a semigroup homomorphism between groups is necessarily a group homomorphism.
 * A ring homomorphism is a map between rings that preserves the ring addition, the ring multiplication, and the multiplicative identity. Whether the multiplicative identity is to be preserved depends upon the definition of ring in use. If the multiplicative identity is not preserved, one has a rng homomorphism.
 * A linear map is a homomorphism of vector spaces; that is, a group homomorphism between vector spaces that preserves the abelian group structure and scalar multiplication.
 * A module homomorphism, also called a linear map between modules, is defined similarly.
 * An algebra homomorphism is a map that preserves the algebra operations.

An algebraic structure may have more than one operation, and a homomorphism is required to preserve each operation. Thus a map that preserves only some of the operations is not a homomorphism of the structure, but only a homomorphism of the substructure obtained by considering only the preserved operations. For example, a map between monoids that preserves the monoid operation and not the identity element, is not a monoid homomorphism, but only a semigroup homomorphism.

The notation for the operations does not need to be the same in the source and the target of a homomorphism. For example, the real numbers form a group for addition, and the positive real numbers form a group for multiplication. The exponential function
 * $$x\mapsto e^x$$

satisfies
 * $$e^{x+y} = e^xe^y,$$

and is thus a homomorphism between these two groups. It is even an isomorphism (see below), as its inverse function, the natural logarithm, satisfies
 * $$\ln(xy)=\ln(x)+\ln(y), $$

and is also a group homomorphism.

Examples
The real numbers are a ring, having both addition and multiplication. The set of all 2×2 matrices is also a ring, under matrix addition and matrix multiplication. If we define a function between these rings as follows:
 * $$f(r) = \begin{pmatrix}

r & 0 \\ 0 & r \end{pmatrix}$$ where $r$ is a real number, then $f$ is a homomorphism of rings, since $f$ preserves both addition:
 * $$f(r+s) = \begin{pmatrix}

r+s & 0 \\ 0 & r+s \end{pmatrix} = \begin{pmatrix} r & 0 \\ 0 & r \end{pmatrix} + \begin{pmatrix} s & 0 \\ 0 & s \end{pmatrix} = f(r) + f(s)$$ and multiplication:
 * $$f(rs) = \begin{pmatrix}

rs & 0 \\ 0 & rs \end{pmatrix} = \begin{pmatrix} r & 0 \\ 0 & r \end{pmatrix} \begin{pmatrix} s & 0 \\ 0 & s \end{pmatrix} = f(r)\,f(s).$$

For another example, the nonzero complex numbers form a group under the operation of multiplication, as do the nonzero real numbers. (Zero must be excluded from both groups since it does not have a multiplicative inverse, which is required for elements of a group.) Define a function $$f$$ from the nonzero complex numbers to the nonzero real numbers by
 * $$f(z) = |z| .$$

That is, $$f$$ is the absolute value (or modulus) of the complex number $$z$$. Then $$f$$ is a homomorphism of groups, since it preserves multiplication:
 * $$f(z_1 z_2) = |z_1 z_2| = |z_1| |z_2| = f(z_1) f(z_2).$$

Note that $(N, +, 0)$ cannot be extended to a homomorphism of rings (from the complex numbers to the real numbers), since it does not preserve addition:
 * $$|z_1 + z_2| \ne |z_1| + |z_2|.$$

As another example, the diagram shows a monoid homomorphism $$f$$ from the monoid $$(\mathbb{N}, +, 0)$$ to the monoid $$(\mathbb{N}, \times, 1)$$. Due to the different names of corresponding operations, the structure preservation properties satisfied by $$f$$ amount to $$f(x+y) = f(x) \times f(y)$$ and $$f(0) = 1$$.

A composition algebra $$A$$ over a field $$F$$ has a quadratic form, called a norm, $$N: A \to F$$, which is a group homomorphism from the multiplicative group of $$A$$ to the multiplicative group of $$F$$.

Special homomorphisms
Several kinds of homomorphisms have a specific name, which is also defined for general morphisms.

Isomorphism
An isomorphism between algebraic structures of the same type is commonly defined as a bijective homomorphism.

In the more general context of category theory, an isomorphism is defined as a morphism that has an inverse that is also a morphism. In the specific case of algebraic structures, the two definitions are equivalent, although they may differ for non-algebraic structures, which have an underlying set.

More precisely, if
 * $$f: A\to B$$

is a (homo)morphism, it has an inverse if there exists a homomorphism
 * $$g: B\to A$$

such that
 * $$f\circ g = \operatorname{Id}_B \qquad \text{and} \qquad g\circ f = \operatorname{Id}_A.$$

If $$A$$ and $$B$$ have underlying sets, and $$f: A \to B$$ has an inverse $$g$$, then $$f$$ is bijective. In fact, $$f$$ is injective, as $$f(x) = f(y)$$ implies $$x = g(f(x)) = g(f(y)) = y$$, and $$f$$ is surjective, as, for any $$x$$ in $$B$$, one has $$x = f(g(x))$$, and $$x$$ is the image of an element of $$A$$.

Conversely, if $$f: A \to B$$ is a bijective homomorphism between algebraic structures, let $$g: B \to A$$ be the map such that $$g(y)$$ is the unique element $$x$$ of $$A$$ such that $$f(x) = y$$. One has $$f \circ g = \operatorname{Id}_B \text{ and } g \circ f = \operatorname{Id}_A,$$ and it remains only to show that $(N, ×, 1)$ is a homomorphism. If $$*$$ is a binary operation of the structure, for every pair $$x$$, $$y$$ of elements of $$B$$, one has
 * $$g(x*_B y) = g(f(g(x))*_Bf(g(y))) = g(f(g(x)*_A g(y))) = g(x)*_A g(y),$$

and $$g$$ is thus compatible with $$*.$$ As the proof is similar for any arity, this shows that $$g$$ is a homomorphism.

This proof does not work for non-algebraic structures. For example, for topological spaces, a morphism is a continuous map, and the inverse of a bijective continuous map is not necessarily continuous. An isomorphism of topological spaces, called homeomorphism or bicontinuous map, is thus a bijective continuous map, whose inverse is also continuous.

Endomorphism
An endomorphism is a homomorphism whose domain equals the codomain, or, more generally, a morphism whose source is equal to its target.

The endomorphisms of an algebraic structure, or of an object of a category form a monoid under composition.

The endomorphisms of a vector space or of a module form a ring. In the case of a vector space or a free module of finite dimension, the choice of a basis induces a ring isomorphism between the ring of endomorphisms and the ring of square matrices of the same dimension.

Automorphism
An automorphism is an endomorphism that is also an isomorphism.

The automorphisms of an algebraic structure or of an object of a category form a group under composition, which is called the automorphism group of the structure.

Many groups that have received a name are automorphism groups of some algebraic structure. For example, the general linear group $$\operatorname{GL}_n(k)$$ is the automorphism group of a vector space of dimension $$n$$ over a field $$k$$.

The automorphism groups of fields were introduced by Évariste Galois for studying the roots of polynomials, and are the basis of Galois theory.

Monomorphism
For algebraic structures, monomorphisms are commonly defined as injective homomorphisms.

In the more general context of category theory, a monomorphism is defined as a morphism that is left cancelable. This means that a (homo)morphism $$f:A \to B$$ is a monomorphism if, for any pair $$g$$, $$h$$ of morphisms from any other object $$C$$ to $$A$$, then $$f \circ g = f \circ h$$ implies $$g = h$$.

These two definitions of monomorphism are equivalent for all common algebraic structures. More precisely, they are equivalent for fields, for which every homomorphism is a monomorphism, and for varieties of universal algebra, that is algebraic structures for which operations and axioms (identities) are defined without any restriction (the fields do not form a variety, as the multiplicative inverse is defined either as a unary operation or as a property of the multiplication, which are, in both cases, defined only for nonzero elements).

In particular, the two definitions of a monomorphism are equivalent for sets, magmas, semigroups, monoids, groups, rings, fields, vector spaces and modules.

A split monomorphism is a homomorphism that has a left inverse and thus it is itself a right inverse of that other homomorphism. That is, a homomorphism $$f\colon A \to B$$ is a split monomorphism if there exists a homomorphism $$g\colon B \to A$$ such that $$g \circ f = \operatorname{Id}_A.$$ A split monomorphism is always a monomorphism, for both meanings of monomorphism. For sets and vector spaces, every monomorphism is a split monomorphism, but this property does not hold for most common algebraic structures.

An injective homomorphism is left cancelable: If $$f\circ g = f\circ h,$$ one has $$f(g(x))=f(h(x))$$ for every $$x$$ in $$C$$, the common source of $$g$$ and $$h$$. If $$f$$ is injective, then $$g(x) = h(x)$$, and thus $$g = h$$. This proof works not only for algebraic structures, but also for any category whose objects are sets and arrows are maps between these sets. For example, an injective continuous map is a monomorphism in the category of topological spaces.

For proving that, conversely, a left cancelable homomorphism is injective, it is useful to consider a free object on $$x$$. Given a variety of algebraic structures a free object on $$x$$ is a pair consisting of an algebraic structure $$L$$ of this variety and an element $$x$$ of $$L$$ satisfying the following universal property: for every structure $$S$$ of the variety, and every element $$s$$ of $$S$$, there is a unique homomorphism $$f: L\to S$$ such that $$f(x) = s$$. For example, for sets, the free object on $$x$$ is simply $$\{x\}$$; for semigroups, the free object on $$x$$ is $$\{x, x^2, \ldots, x^n, \ldots\},$$ which, as, a semigroup, is isomorphic to the additive semigroup of the positive integers; for monoids, the free object on $$x$$ is $$\{1, x, x^2, \ldots, x^n, \ldots\},$$ which, as, a monoid, is isomorphic to the additive monoid of the nonnegative integers; for groups, the free object on $$x$$ is the infinite cyclic group $$\{\ldots, x^{-n}, \ldots, x^{-1}, 1, x, x^2, \ldots, x^n, \ldots\},$$ which, as, a group, is isomorphic to the additive group of the integers; for rings, the free object on $$x$$ is the polynomial ring $$\mathbb{Z}[x];$$ for vector spaces or modules, the free object on $$x$$ is the vector space or free module that has $$x$$ as a basis.

If a free object over $$x$$ exists, then every left cancelable homomorphism is injective: let $$f\colon A \to B$$ be a left cancelable homomorphism, and $$a$$ and $$b$$ be two elements of $$A$$ such $$f(a) = f(b)$$. By definition of the free object $$F$$, there exist homomorphisms $$g$$ and $$h$$ from $$F$$ to $$A$$ such that $$g(x) = a$$ and $$h(x) = b$$. As $$f(g(x)) = f(h(x))$$, one has $$f \circ g = f \circ h, $$ by the uniqueness in the definition of a universal property. As $$f$$ is left cancelable, one has $$g = h$$, and thus $$a = b$$. Therefore, $$f$$ is injective.

Existence of a free object on $$x$$ for a variety (see also ): For building a free object over $$x$$, consider the set $$W$$ of the well-formed formulas built up from $$x$$ and the operations of the structure. Two such formulas are said equivalent if one may pass from one to the other by applying the axioms (identities of the structure). This defines an equivalence relation, if the identities are not subject to conditions, that is if one works with a variety. Then the operations of the variety are well defined on the set of equivalence classes of $$W$$ for this relation. It is straightforward to show that the resulting object is a free object on $$x$$.

Epimorphism
In algebra, epimorphisms are often defined as surjective homomorphisms. On the other hand, in category theory, epimorphisms are defined as right cancelable morphisms. This means that a (homo)morphism $$f: A \to B$$ is an epimorphism if, for any pair $$g$$, $$h$$ of morphisms from $$B$$ to any other object $$C$$, the equality $$g \circ f = h \circ f$$ implies $$g = h$$.

A surjective homomorphism is always right cancelable, but the converse is not always true for algebraic structures. However, the two definitions of epimorphism are equivalent for sets, vector spaces, abelian groups, modules (see below for a proof), and groups. The importance of these structures in all mathematics, especially in linear algebra and homological algebra, may explain the coexistence of two non-equivalent definitions.

Algebraic structures for which there exist non-surjective epimorphisms include semigroups and rings. The most basic example is the inclusion of integers into rational numbers, which is a homomorphism of rings and of multiplicative semigroups. For both structures it is a monomorphism and a non-surjective epimorphism, but not an isomorphism.

A wide generalization of this example is the localization of a ring by a multiplicative set. Every localization is a ring epimorphism, which is not, in general, surjective. As localizations are fundamental in commutative algebra and algebraic geometry, this may explain why in these areas, the definition of epimorphisms as right cancelable homomorphisms is generally preferred.

A split epimorphism is a homomorphism that has a right inverse and thus it is itself a left inverse of that other homomorphism. That is, a homomorphism $$f\colon A \to B$$ is a split epimorphism if there exists a homomorphism $$g\colon B \to A$$ such that $$f\circ g = \operatorname{Id}_B.$$ A split epimorphism is always an epimorphism, for both meanings of epimorphism. For sets and vector spaces, every epimorphism is a split epimorphism, but this property does not hold for most common algebraic structures.

In summary, one has
 * $$\text {split epimorphism} \implies \text{epimorphism (surjective)}\implies \text {epimorphism (right cancelable)};$$

the last implication is an equivalence for sets, vector spaces, modules, abelian groups, and groups; the first implication is an equivalence for sets and vector spaces.

Let $$f\colon A \to B$$ be a homomorphism. We want to prove that if it is not surjective, it is not right cancelable.

In the case of sets, let $$b$$ be an element of $$B$$ that not belongs to $$f(A)$$, and define $$g, h\colon B \to B$$ such that $$g$$ is the identity function, and that $$h(x) = x$$ for every $$x \in B,$$ except that $$h(b)$$ is any other element of $$B$$. Clearly $$f$$ is not right cancelable, as $$g \neq h$$ and $$g \circ f = h \circ f.$$

In the case of vector spaces, abelian groups and modules, the proof relies on the existence of cokernels and on the fact that the zero maps are homomorphisms: let $$C$$ be the cokernel of $$f$$, and $$g\colon B \to C$$ be the canonical map, such that $$g(f(A)) = 0$$. Let $$h\colon B\to C$$ be the zero map. If $$f$$ is not surjective, $$C \neq 0$$, and thus $$g \neq h$$ (one is a zero map, while the other is not). Thus $$f$$ is not cancelable, as $$g \circ f = h \circ f$$ (both are the zero map from $$A$$ to $$C$$).

Kernel
Any homomorphism $$f: X \to Y$$ defines an equivalence relation $$\sim$$ on $$X$$ by $$a \sim b$$ if and only if $$f(a) = f(b)$$. The relation $$\sim$$ is called the kernel of $$f$$. It is a congruence relation on $$X$$. The quotient set $$X/{\sim}$$ can then be given a structure of the same type as $$X$$, in a natural way, by defining the operations of the quotient set by $$[x] \ast [y] = [x \ast y]$$, for each operation $$\ast$$ of $$X$$. In that case the image of $$X$$ in $$Y$$ under the homomorphism $$f$$ is necessarily isomorphic to $$X/\!\sim$$; this fact is one of the isomorphism theorems.

When the algebraic structure is a group for some operation, the equivalence class $$K$$ of the identity element of this operation suffices to characterize the equivalence relation. In this case, the quotient by the equivalence relation is denoted by $$X/K$$ (usually read as "$$X$$ mod $$K$$"). Also in this case, it is $$K$$, rather than $$\sim$$, that is called the kernel of $$f$$. The kernels of homomorphisms of a given type of algebraic structure are naturally equipped with some structure. This structure type of the kernels is the same as the considered structure, in the case of abelian groups, vector spaces and modules, but is different and has received a specific name in other cases, such as normal subgroup for kernels of group homomorphisms and ideals for kernels of ring homomorphisms (in the case of non-commutative rings, the kernels are the two-sided ideals).

Relational structures
In model theory, the notion of an algebraic structure is generalized to structures involving both operations and relations. Let L be a signature consisting of function and relation symbols, and A, B be two L-structures. Then a homomorphism from A to B is a mapping h from the domain of A to the domain of B such that In the special case with just one binary relation, we obtain the notion of a graph homomorphism.
 * h(FA(a1,…,an)) = FB(h(a1),…,h(an)) for each n-ary function symbol F in L,
 * RA(a1,…,an) implies RB(h(a1),…,h(an)) for each n-ary relation symbol R in L.

Formal language theory
Homomorphisms are also used in the study of formal languages and are often briefly referred to as morphisms. Given alphabets $$\Sigma_1$$ and $$\Sigma_2$$, a function $$h \colon \Sigma_1^* \to \Sigma_2^*$$ such that $$h(uv) = h(u) h(v)$$ for all $$u,v \in \Sigma_1$$ is called a homomorphism on $$\Sigma_1^*$$. If $$h$$ is a homomorphism on $$\Sigma_1^*$$ and $$\varepsilon$$ denotes the empty string, then $$h$$ is called an $$\varepsilon$$-free homomorphism when $$h(x) \neq \varepsilon$$ for all $$x \neq \varepsilon$$ in $$\Sigma_1^*$$.

A homomorphism $$h \colon \Sigma_1^* \to \Sigma_2^*$$ on $$\Sigma_1^*$$ that satisfies $$|h(a)| = k$$ for all $$a \in \Sigma_1$$ is called a $$k$$-uniform homomorphism. If $$|h(a)| = 1$$ for all $$a \in \Sigma_1$$ (that is, $$h$$ is 1-uniform), then $$h$$ is also called a coding or a projection.

The set $$\Sigma^*$$ of words formed from the alphabet $$\Sigma$$ may be thought of as the free monoid generated by $$\Sigma$$. Here the monoid operation is concatenation and the identity element is the empty word. From this perspective, a language homomorphism is precisely a monoid homomorphism.

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

title: Homomorphism


text:
HyperCard

HyperCard is a software application and development kit for Apple Macintosh and Apple IIGS computers. It is among the first successful hypermedia systems predating the World Wide Web.

HyperCard combines a flat-file database with a graphical, flexible, user-modifiable interface. HyperCard includes a built-in programming language called HyperTalk for manipulating data and the user interface.

This combination of features – a database with simple form layout, flexible support for graphics, and ease of programming – suits HyperCard for many different projects such as rapid application development of applications and databases, interactive applications with no database requirements, command and control systems, and many examples in the demoscene.

HyperCard was originally released in 1987 for $49.95 and was included free with all new Macs sold afterwards. It was withdrawn from sale in March 2004, having received its final update in 1998 upon the return of Steve Jobs to Apple. HyperCard was not ported to Mac OS X, but can run in the Classic Environment on versions of Mac OS X that support it.

Design

HyperCard is based on the concept of a "stack" of virtual "cards". Cards hold data, just as they would in a Rolodex card-filing device. Each card contains a set of interactive objects, including text fields, check boxes, buttons, and similar common graphical user interface (GUI) elements. Users browse the stack by navigating from card to card, using built-in navigation features, a powerful search mechanism, or through user-created scripts.

Users build or modify stacks by adding new cards. They place GUI objects on the cards using an interactive layout engine based on a simple drag-and-drop interface. Also, HyperCard includes prototype or template cards called backgrounds; when new cards are created they can refer to one of these background cards, which causes all of the objects on the background to "show through" behind the new card. This way, a stack of cards with a common layout and functionality can be created. The layout engine is similar in concept to a form as used in most rapid application development (RAD) environments such as Borland Delphi, and Microsoft Visual Basic and Visual Studio.

The database features of the HyperCard system are based on the storage of the state of all of the objects on the cards in the physical file representing the stack. The database does not exist as a separate system within the HyperCard stack; no database engine or similar construct exists. Instead, the state of any object in the system is considered to be live and editable at any time. From the HyperCard runtime's perspective, there is no difference between moving a text field on the card and typing into it; both operations simply change the state of the target object within the stack. Such changes are immediately saved when complete, so typing into a field causes that text to be stored to the stack's physical file. The system operates in a largely stateless fashion, with no need to save during operation. This is in common with many database-oriented systems, although somewhat different from document-based applications.

The final key element in HyperCard is the script, a single code-carrying element of every object within the stack. The script is a text field whose contents are interpreted in the HyperTalk language. Like any other property, the script of any object can be edited at any time and changes are saved as soon as they were complete. When the user invokes actions in the GUI, like clicking on a button or typing into a field, these actions are translated into events by the HyperCard runtime. The runtime then examines the script of the object that is the target of the event, like a button, to see if its script object contains the event's code, called a handler. If it does, the HyperTalk engine runs the handler; if it does not, the runtime examines other objects in the visual hierarchy.

These concepts make up the majority of the HyperCard system; stacks, backgrounds and cards provide a form-like GUI system, the stack file provides object persistence and database-like functionality, and HyperTalk allows handlers to be written for GUI events. Unlike the majority of RAD or database systems of the era, however, HyperCard combines all of these features, both user-facing and developer-facing, in a single application. This allows rapid turnaround and immediate prototyping, possibly without any coding, allowing users to author custom solutions to problems with their own personalized interface. "Empowerment" became a catchword as this possibility was embraced by the Macintosh community, as was the phrase "programming for the rest of us", that is, anyone, not just professional programmers.

It is this combination of features that also makes HyperCard a powerful hypermedia system. Users can build backgrounds to suit the needs of some system, say a rolodex, and use simple HyperTalk commands to provide buttons to move from place to place within the stack, or provide the same navigation system within the data elements of the UI, like text fields. Using these features, it is easy to build linked systems similar to hypertext links on the Web. Unlike the Web, programming, placement, and browsing are all the same tool. Similar systems have been created for HTML, but traditional Web services are considerably more heavyweight.

HyperTalk
HyperCard contains an object-oriented scripting language called HyperTalk, which was noted for having a syntax resembling casual English language. HyperTalk language features were predetermined by the HyperCard environment, although they could be extended by the use of externals functions (XFCN) and commands (XCMD), written in a compiled language. The weakly typed HyperTalk supports most standard programming structures such as "if–then" and "repeat". HyperTalk is verbose, hence its ease of use and readability. HyperTalk code segments are referred to as "scripts", a term that is considered less daunting to beginning programmers.

Externals
HyperCard can be extended significantly through the use of external command (XCMD) and external function (XFCN) modules. These are code libraries packaged in a resource fork that integrate into either the system generally or the HyperTalk language specifically; this is an early example of the plug-in concept. Unlike conventional plug-ins, these do not require separate installation before they are available for use; they can be included in a stack, where they are directly available to scripts in that stack.

During HyperCard's peak popularity in the late 1980s, a whole ecosystem of vendors offered thousands of these externals such as HyperTalk compilers, graphing systems, database access, Internet connectivity, and animation. Oracle offered an XCMD that allows HyperCard to directly query Oracle databases on any platform, superseded by Oracle Card. BeeHive Technologies offered a hardware interface that allows the computer to control external devices. Connected via the Apple Desktop Bus (ADB), this instrument can read the state of connected external switches or write digital outputs to a multitude of devices.

Externals allow access to the Macintosh Toolbox, which contains many lower-level commands and functions not native to HyperTalk, such as control of the serial and ADB ports.

Development
HyperCard was created by Bill Atkinson following an LSD trip. Work for it began in March 1985 under the name of WildCard (hence its creator code of WILD). In 1986, Dan Winkler began work on HyperTalk and the name was changed to HyperCard for trademark reasons. It was released on 11 August 1987 for the first day of the MacWorld Conference & Expo in Boston, with the understanding that Atkinson would give HyperCard to Apple only if the company promised to release it for free on all Macs. Apple timed its release to coincide with the MacWorld Conference & Expo in Boston, Massachusetts to guarantee maximum publicity.

Launch
HyperCard was successful almost instantly. The Apple Programmer's and Developer's Association (APDA) said, "HyperCard has been an informational feeding frenzy. From August [1987, when it was announced] to October our phones never stopped ringing. It was a zoo." Within a few months of release, there were multiple HyperCard books and a 50 disk set of public domain stacks. Apple's project managers found HyperCard was being used by a huge number of people, internally and externally. Bug reports and upgrade suggestions continued to flow in, demonstrating its wide variety of users. Since it was also free, it was difficult to justify dedicating engineering resources to improvements in the software. Apple and its mainstream developers understood that HyperCard's user empowerment could reduce the sales of ordinary shrink-wrapped products. Stewart Alsop II speculated that HyperCard might replace Finder as the shell of the Macintosh graphical user interface.

HyperCard 2.0
In late 1989, Kevin Calhoun, then a HyperCard engineer at Apple, led an effort to upgrade the program. This resulted in HyperCard 2.0, released in 1990. The new version included an on-the-fly compiler that greatly increased performance of computationally intensive code, a new debugger and many improvements to the underlying HyperTalk language.

At the same time HyperCard 2.0 was being developed, a separate group within Apple developed and in 1991 released HyperCard IIGS, a version of HyperCard for the Apple IIGS system. Aimed mainly at the education market, HyperCard IIGS has roughly the same feature set as the 1.x versions of Macintosh HyperCard, while adding support for the color graphics abilities of the IIGS. Although stacks (HyperCard program documents) are not binary-compatible, a translator program (another HyperCard stack) allows them to be moved from one platform to the other.

Then, Apple decided that most of its application software packages, including HyperCard, would be the property of a wholly owned subsidiary called Claris. Many of the HyperCard developers chose to stay at Apple rather than move to Claris, causing the development team to be split. Claris attempted to create a business model where HyperCard could also generate revenues. At first the freely-distributed versions of HyperCard shipped with authoring disabled. Early versions of Claris HyperCard contain an Easter Egg: typing "magic" into the message box converts the player into a full HyperCard authoring environment. When this trick became nearly universal, they wrote a new version, HyperCard Player, which Apple distributed with the Macintosh operating system, while Claris sold the full version commercially. Many users were upset that they had to pay to use software that had traditionally been supplied free and which many considered a basic part of the Mac.

Even after HyperCard was generating revenue, Claris did little to market it. Development continued with minor upgrades, and the first failed attempt to create a third generation of HyperCard. During this period, HyperCard began losing market share. Without several important, basic features, HyperCard authors began moving to systems such as SuperCard and Macromedia Authorware. Nonetheless, HyperCard continued to be popular and used for a widening range of applications, from the game The Manhole, an earlier effort by the creators of Myst, to corporate information services.

Apple eventually folded Claris back into the parent company, returning HyperCard to Apple's core engineering group. In 1992, Apple released the eagerly anticipated upgrade of HyperCard 2.2 and included licensed versions of Color Tools and Addmotion II, adding support for color pictures and animations. However, these tools are limited and often cumbersome to use because HyperCard 2.0 lacks true, internal color support.

HyperCard 3.0
Several attempts were made to restart HyperCard development once it returned to Apple. Because of the product's widespread use as a multimedia-authoring tool it was rolled into the QuickTime group. A new effort to allow HyperCard to create QuickTime interactive (QTi) movies started, once again under the direction of Kevin Calhoun. QTi extended QuickTime's core multimedia playback features to provide true interactive facilities and a low-level programming language based on 68000 assembly language. The resulting HyperCard 3.0 was first presented in 1996 when an alpha-quality version was shown to developers at Apple's annual Apple Worldwide Developers Conference (WWDC). Under the leadership of Dan Crow development continued through the late 1990s, with public demos showing many popular features such as color support, Internet connectivity, and the ability to play HyperCard stacks (which were now special QuickTime movies) in a web browser. Development upon HyperCard 3.0 stalled when the QuickTime team was focused away from developing QuickTime interactive to the streaming features of QuickTime 4.0. in 1998 Steve Jobs disliked the software because Atkinson had chosen to stay at Apple to finish it instead of joining Jobs at NeXT, and (according to Atkinson) "it had Sculley's stink all over it". In 2000, the HyperCard engineering team was reassigned to other tasks after Jobs decided to abandon the product. Calhoun and Crow both left Apple shortly after, in 2001.

Its final release was in 1998, and it was totally discontinued in March 2004.

HyperCard runs natively only in the classic Mac OS, but it can still be used in Mac OS X's Classic mode on PowerPC based machines (G5 and earlier). The last functional native HyperCard authoring environment is Classic mode in Mac OS X 10.4 (Tiger) on PowerPC-based machines.

Applications
HyperCard has been used for a range of hypertext and artistic purposes. Before the advent of PowerPoint, HyperCard was often used as a general-purpose presentation program. Examples of HyperCard applications include simple databases, "choose your own adventure"-type games, and educational teaching aids.

Due to its rapid application design facilities, HyperCard was also often used for prototyping applications and sometimes even for version 1.0 implementations. Inside Apple, the QuickTime team was one of HyperCard's biggest customers.

HyperCard has lower hardware requirements than Macromedia Director. Several commercial software products were created in HyperCard, most notably the original version of the graphic adventure game Myst, the Voyager Company's Expanded Books, multimedia CD-ROMs of Beethoven's Ninth Symphony CD-ROM, A Hard Day's Night by the Beatles, and the Voyager MacBeth. An early electronic edition of the Whole Earth Catalog was implemented in HyperCard. and stored on CD-ROM.

The prototype and demo of the popular game You Don't Know Jack was written in HyperCard. The French auto manufacturer Renault used it to control their inventory system.

In Quebec, Canada, HyperCard was used to control a robot arm used to insert and retrieve video disks at the National Film Board CinéRobothèque.

In 1989, Hypercard was used to control the BBC Radiophonic Workshop Studio Network, using a single Macintosh.

HyperCard was used to prototype a fully functional prototype of SIDOCI (one of the first experiments in the world to develop an integrated electronic patient record system) and was heavily used by Montréal Consulting firm DMR to demonstrate how "a typical day in the life of a patient about to get surgery" would look like in a paperless age.

Activision, which was until then mainly a game company, saw HyperCard as an entry point into the business market. Changing its name to Mediagenic, it published several major HyperCard-based applications, most notably Danny Goodman's Focal Point, a personal information manager, and Reports For HyperCard, a program by Nine To Five Software that allows users to treat HyperCard as a full database system with robust information viewing and printing features.

The HyperCard-inspired SuperCard for a while included the Roadster plug-in that allowed stacks to be placed inside web pages and viewed by web browsers with an appropriate browser plug-in. There was even a Windows version of this plug-in allowing computers other than Macintoshes to use the plug-in.

Exploits
The first HyperCard virus was discovered in Belgium and the Netherlands in April 1991.

Because HyperCard executed scripts in stacks immediately on opening, it was also one of the first applications susceptible to macro viruses. The Merryxmas virus was discovered in early 1993 by Ken Dunham, two years before the Concept virus. Very few viruses were based on HyperCard, and their overall impact was minimal.

Reception
Compute!'s Apple Applications in 1987 stated that HyperCard "may make Macintosh the personal computer of choice". While noting that its large memory requirement made it best suited for computers with 2 MB of memory and hard drives, the magazine predicted that "the smallest programming shop should be able to turn out stackware", especially for using CD-ROMs. Compute! predicted in 1988 that most future Mac software would be developed using HyperCard, if only because using it was so addictive that developers "won't be able to tear themselves away from it long enough to create anything else". Byte in 1989 listed it as among the "Excellence" winners of the Byte Awards. While stating that "like any first entry, it has some flaws", the magazine wrote that "HyperCard opened up a new category of software", and praised Apple for bundling it with every Mac. In 2001 Steve Wozniak called HyperCard "the best program ever written".

Legacy
HyperCard is one of the first products that made use of and popularized the hypertext concept to a large popular base of users.

Jakob Nielsen has pointed out that HyperCard was really only a hypermedia program since its links started from regions on a card, not text objects; actual HTML-style text hyperlinks were possible in later versions, but were awkward to implement and seldom used. Deena Larsen programmed links into HyperCard for Marble Springs. Bill Atkinson later lamented that if he had only realized the power of network-oriented stacks, instead of focusing on local stacks on a single machine, HyperCard could have become the first Web browser.

HyperCard saw a loss in popularity with the growth of the World Wide Web, since the Web could handle and deliver data in much the same way as HyperCard without being limited to files on a local hard disk. HyperCard had a significant impact on the web as it inspired the creation of both HTTP (through its influence on Tim Berners-Lee's colleague Robert Cailliau), and JavaScript (whose creator, Brendan Eich, was inspired by HyperTalk ). It was also a key inspiration for ViolaWWW, an early web browser.

The pointing-finger cursor used for navigating stacks was later used in the first web browsers, as the hyperlink cursor.

The Myst computer game franchise, initially released as a HyperCard stack and included bundled with some Macs (for example the Performa 5300), still lives on, making HyperCard a facilitating technology for starting one of the best-selling computer games of all time.

According to Ward Cunningham, the inventor of Wiki, the wiki concept can be traced back to a HyperCard stack he wrote in the late 1980s.

In 2017 the Internet Archive established a project to preserve and emulate HyperCard stacks, allowing users to upload their own.

The GUI of the prototype Apple Wizzy Active Lifestyle Telephone was based on HyperCard.

World Wide Web
HyperCard influenced the development of the Web in late 1990 through its influence on Robert Cailliau, who assisted in developing Tim Berners-Lee's first Web browser. Javascript was inspired by HyperTalk.

Although HyperCard stacks do not operate over the Internet, by 1988, at least 300 stacks were publicly available for download from the commercial CompuServe network (which was not connected to the official Internet yet). The system can link phone numbers on a user's computer together and enable them to dial numbers without a modem, using a less expensive piece of hardware, the Hyperdialer.

In this sense, like the Web, it does form an association-based experience of information browsing via links, though not operating remotely over the TCP/IP protocol then. Like the Web, it also allows for the connections of many different kinds of media.

Similar systems
Other companies have offered their own versions. , four products are available which offer HyperCard-like abilities:
 * HyperStudio, one of the first HyperCard clones, is, developed and published by Software MacKiev.
 * LiveCode, published by LiveCode, Ltd., expands greatly on HyperCard's feature set and offers color and a GUI toolkit which can be deployed on many popular platforms (Android, iOS, Classic Macintosh system software, Mac OS X, Windows 98 through 10, and Linux/Unix). LiveCode directly imports extant HyperCard stacks and provides a migration path for stacks still in use.
 * SuperCard, the first HyperCard clone, is similar to HyperCard, but with many added features such as: full color support, pixel and vector graphics, a full GUI toolkit, and support for many modern Mac OS X features. It can create both standalone applications and projects that run on the freeware SuperCard Player. SuperCard can also convert extant HyperCard stacks into SuperCard projects. It runs only on Macs.

Past products include:
 * SK8 was a "HyperCard killer" developed within Apple but never released. It extends HyperTalk to allow arbitrary objects which allowed it to build complete Mac-like applications (instead of stacks). The project was never released, although the source code was placed in the public domain.
 * Hyper DA by Symmetry was a Desk Accessory for classic single-tasked Mac OS that allows viewing HyperCard 1.x stacks as added windows in any extant application, and is also embedded into many Claris products (like MacDraw II) to display their user documentation.
 * HyperPad from Brightbill-Roberts is a clone of HyperCard, written for DOS. It makes use of ASCII linedrawing to create the graphics of cards and buttons.
 * Plus, later renamed WinPlus, is similar to HyperCard, for Windows and Macintosh.
 * Oracle purchased Plus and created a cross-platform version as Oracle Card, later renamed Oracle Media Objects, used as a 4GL for database access.
 * IBM LinkWay - a mouse-controlled HyperCard-like environment for DOS PCs. It has minimal system requirements, runs in graphics CGA and VGA. It even supported video disc control.
 * Asymetrix's Windows application ToolBook resembles HyperCard, and later included an external converter to read HyperCard stacks (the first was a third-party product from Heizer software).
 * TileStack is an attempt to create a web based version of HyperCard that is compatible with the original HyperCard files. The site closed down January 24, 2011.

In addition, many of the basic concepts of the original system were later re-used in other forms. Apple built its system-wide scripting engine AppleScript on a language similar to HyperTalk; it is often used for desktop publishing (DTP) workflow automation needs. In the 1990s FaceSpan provided a third-party graphical interface. AppleScript also has a native graphical programming front-end called Automator, released with Mac OS X Tiger in April 2005. One of HyperCard's strengths was its handling of multimedia, and many multimedia systems like Macromedia Authorware and Macromedia Director are based on concepts originating in HyperCard.

AppWare, originally named Serius Developer, is sometimes seen to be similar to HyperCard, as both are rapid application development (RAD) systems. AppWare was sold in the early 90s and worked on both Mac and Windows systems.

Zoomracks, a DOS application with a similar "stack" database metaphor, predates HyperCard by 4 years, which led to a contentious lawsuit against Apple.

title: HyperCard


text:
Histology

Histology, also known as microscopic anatomy or microanatomy, is the branch of biology that studies the microscopic anatomy of biological tissues. Histology is the microscopic counterpart to gross anatomy, which looks at larger structures visible without a microscope. Although one may divide microscopic anatomy into organology, the study of organs, histology, the study of tissues, and cytology, the study of cells, modern usage places all of these topics under the field of histology. In medicine, histopathology is the branch of histology that includes the microscopic identification and study of diseased tissue. In the field of paleontology, the term paleohistology refers to the histology of fossil organisms.

Animal tissue classification
There are four basic types of animal tissues: muscle tissue, nervous tissue, connective tissue, and epithelial tissue. All animal tissues are considered to be subtypes of these four principal tissue types (for example, blood is classified as connective tissue, since the blood cells are suspended in an extracellular matrix, the plasma). • Epithelium

• * Simple epithelium

• ** Simple squamous epithelium

• ** Simple cuboidal epithelium

• ** Simple columnar epithelium

• * Pseudostratified columnar epithelium

• * Stratified epithelium

• ** Stratified squamous epithelium

• ** Stratified cuboidal epithelium

• ** Stratified columnar epithelium

• ** Transitional epithelium

• * Multicellular glands

• Muscle tissue

• * Smooth muscle

• * Skeletal muscle

• * Cardiac muscle

• Connective tissue

• * General connective tissue

• ** Loose connective tissue

• ** Dense connective tissue

• * Special connective tissue

• ** Cartilage

• ** Bone

• ** Hemopoietic

• ** Blood

• ** Lymph

• Nervous tissue

• * Central nervous system

• * Peripheral nervous system

• * Special receptors

Plant tissue classification

For plants, the study of their tissues falls under the field of plant anatomy, with the following four main types:
 * Dermal tissue
 * Vascular tissue
 * Ground tissue
 * Meristematic tissue

Medical histology
Histopathology is the branch of histology that includes the microscopic identification and study of diseased tissue. It is an important part of anatomical pathology and surgical pathology, as accurate diagnosis of cancer and other diseases often requires histopathological examination of tissue samples. Trained physicians, frequently licensed pathologists, perform histopathological examination and provide diagnostic information based on their observations.

Occupations
The field of histology that includes the preparation of tissues for microscopic examination is known as histotechnology. Job titles for the trained personnel who prepare histological specimens for examination are numerous and include histotechnicians, histotechnologists, histology technicians and technologists, medical laboratory technicians, and biomedical scientists.

Sample preparation
Most histological samples need preparation before microscopic observation; these methods depend on the specimen and method of observation.

Fixation

Chemical fixatives are used to preserve and maintain the structure of tissues and cells; fixation also hardens tissues which aids in cutting the thin sections of tissue needed for observation under the microscope. Fixatives generally preserve tissues (and cells) by irreversibly cross-linking proteins. The most widely used fixative for light microscopy is 10% neutral buffered formalin, or NBF (4% formaldehyde in phosphate buffered saline).

For electron microscopy, the most commonly used fixative is glutaraldehyde, usually as a 2.5% solution in phosphate buffered saline. Other fixatives used for electron microscopy are osmium tetroxide or uranyl acetate.

The main action of these aldehyde fixatives is to cross-link amino groups in proteins through the formation of methylene bridges (-CH2-), in the case of formaldehyde, or by C5H10 cross-links in the case of glutaraldehyde. This process, while preserving the structural integrity of the cells and tissue can damage the biological functionality of proteins, particularly enzymes.

Formalin fixation leads to degradation of mRNA, miRNA, and DNA as well as denaturation and modification of proteins in tissues. However, extraction and analysis of nucleic acids and proteins from formalin-fixed, paraffin-embedded tissues is possible using appropriate protocols.

Selection and trimming
Selection is the choice of relevant tissue in cases where it is not necessary to put the entire original tissue mass through further processing. The remainder may remain fixed in case it needs to be examined at a later time.

Trimming is the cutting of tissue samples in order to expose the relevant surfaces for later sectioning. It also creates tissue samples of appropriate size to fit into cassettes.

Embedding
Tissues are embedded in a harder medium both as a support and to allow the cutting of thin tissue slices. In general, water must first be removed from tissues (dehydration) and replaced with a medium that either solidifies directly, or with an intermediary fluid (clearing) that is miscible with the embedding media.

Paraffin wax

For light microscopy, paraffin wax is the most frequently used embedding material. Paraffin is immiscible with water, the main constituent of biological tissue, so it must first be removed in a series of dehydration steps. Samples are transferred through a series of progressively more concentrated ethanol baths, up to 100% ethanol to remove remaining traces of water. Dehydration is followed by a clearing agent (typically xylene although other environmental safe substitutes are in use ) which removes the alcohol and is miscible with the wax, finally melted paraffin wax is added to replace the xylene and infiltrate the tissue. In most histology, or histopathology laboratories the dehydration, clearing, and wax infiltration are carried out in tissue processors which automate this process. Once infiltrated in paraffin, tissues are oriented in molds which are filled with wax; once positioned, the wax is cooled, solidifying the block and tissue.

Other materials
Paraffin wax does not always provide a sufficiently hard matrix for cutting very thin sections (which are especially important for electron microscopy). Paraffin wax may also be too soft in relation to the tissue, the heat of the melted wax may alter the tissue in undesirable ways, or the dehydrating or clearing chemicals may harm the tissue. Alternatives to paraffin wax include, epoxy, acrylic, agar, gelatin, celloidin, and other types of waxes.

In electron microscopy epoxy resins are the most commonly employed embedding media, but acrylic resins are also used, particularly where immunohistochemistry is required.

For tissues to be cut in a frozen state, tissues are placed in a water-based embedding medium. Pre-frozen tissues are placed into molds with the liquid embedding material, usually a water-based glycol, OCT, TBS, Cryogen, or resin, which is then frozen to form hardened blocks.

Sectioning

For light microscopy, a knife mounted in a microtome is used to cut tissue sections (typically between 5-15 micrometers thick) which are mounted on a glass microscope slide. For transmission electron microscopy (TEM), a diamond or glass knife mounted in an ultramicrotome is used to cut between 50 and 150 nanometer thick tissue sections.

A limited number of manufacturers are recognized for their production of microtomes, including vibrating microtomes commonly referred to as vibratomes, primarily for research and clinical studies. Additionally, Leica Biosystems is known for its production of products related to light microscopy in the context of research and clinical studies.

Staining
Biological tissue has little inherent contrast in either the light or electron microscope. Staining is employed to give both contrast to the tissue as well as highlighting particular features of interest. When the stain is used to target a specific chemical component of the tissue (and not the general structure), the term histochemistry is used.

Light microscopy
Hematoxylin and eosin (H&E stain) is one of the most commonly used stains in histology to show the general structure of the tissue. Hematoxylin stains cell nuclei blue; eosin, an acidic dye, stains the cytoplasm and other tissues in different stains of pink.

In contrast to H&E, which is used as a general stain, there are many techniques that more selectively stain cells, cellular components, and specific substances. A commonly performed histochemical technique that targets a specific chemical is the Perls' Prussian blue reaction, used to demonstrate iron deposits in diseases like hemochromatosis. The Nissl method for Nissl substance and Golgi's method (and related silver stains) are useful in identifying neurons are other examples of more specific stains.

Historadiography
In historadiography, a slide (sometimes stained histochemically) is X-rayed. More commonly, autoradiography is used in visualizing the locations to which a radioactive substance has been transported within the body, such as cells in S phase (undergoing DNA replication) which incorporate tritiated thymidine, or sites to which radiolabeled nucleic acid probes bind in in situ hybridization. For autoradiography on a microscopic level, the slide is typically dipped into liquid nuclear tract emulsion, which dries to form the exposure film. Individual silver grains in the film are visualized with dark field microscopy.

Immunohistochemistry
Recently, antibodies have been used to specifically visualize proteins, carbohydrates, and lipids. This process is called immunohistochemistry, or when the stain is a fluorescent molecule, immunofluorescence. This technique has greatly increased the ability to identify categories of cells under a microscope. Other advanced techniques, such as nonradioactive in situ hybridization, can be combined with immunochemistry to identify specific DNA or RNA molecules with fluorescent probes or tags that can be used for immunofluorescence and enzyme-linked fluorescence amplification (especially alkaline phosphatase and tyramide signal amplification). Fluorescence microscopy and confocal microscopy are used to detect fluorescent signals with good intracellular detail.

Electron microscopy
For electron microscopy heavy metals are typically used to stain tissue sections. Uranyl acetate and lead citrate are commonly used to impart contrast to tissue in the electron microscope.

Cryosectioning
Similar to the frozen section procedure employed in medicine, cryosectioning is a method to rapidly freeze, cut, and mount sections of tissue for histology. The tissue is usually sectioned on a cryostat or freezing microtome. The frozen sections are mounted on a glass slide and may be stained to enhance the contrast between different tissues. Unfixed frozen sections can be used for studies requiring enzyme localization in tissues and cells. Tissue fixation is required for certain procedures such as antibody-linked immunofluorescence staining. Frozen sections are often prepared during surgical removal of tumors to allow rapid identification of tumor margins, as in Mohs surgery, or determination of tumor malignancy, when a tumor is discovered incidentally during surgery.

Ultramicrotomy

Ultramicrotomy is a method of preparing extremely thin sections for transmission electron microscope (TEM) analysis. Tissues are commonly embedded in epoxy or other plastic resin. Very thin sections (less than 0.1 micrometer in thickness) are cut using diamond or glass knives on an ultramicrotome.

Artifacts
Artifacts are structures or features in tissue that interfere with normal histological examination. Artifacts interfere with histology by changing the tissues appearance and hiding structures. Tissue processing artifacts can include pigments formed by fixatives, shrinkage, washing out of cellular components, color changes in different tissues types and alterations of the structures in the tissue. An example is mercury pigment left behind after using Zenker's fixative to fix a section. Formalin fixation can also leave a brown to black pigment under acidic conditions.

History
In the 17th century the Italian Marcello Malpighi used microscopes to study tiny biological entities; some regard him as the founder of the fields of histology and microscopic pathology. Malpighi analyzed several parts of the organs of bats, frogs and other animals under the microscope. While studying the structure of the lung, Malpighi noticed its membranous alveoli and the hair-like connections between veins and arteries, which he named capillaries. His discovery established how the oxygen breathed in enters the blood stream and serves the body.

In the 19th century histology was an academic discipline in its own right. The French anatomist Xavier Bichat introduced the concept of tissue in anatomy in 1801, and the term "histology" (Histologie), coined to denote the "study of tissues", first appeared in a book by Karl Meyer in 1819. Bichat described twenty-one human tissues, which can be subsumed under the four categories currently accepted by histologists. The usage of illustrations in histology, deemed as useless by Bichat, was promoted by Jean Cruveilhier.

In the early 1830s Purkynĕ invented a microtome with high precision.

During the 19th century many fixation techniques were developed by Adolph Hannover (solutions of chromates and chromic acid), Franz Schulze and Max Schultze (osmic acid), Alexander Butlerov (formaldehyde) and Benedikt Stilling (freezing).

Mounting techniques were developed by Rudolf Heidenhain (1824-1898), who introduced gum Arabic; Salomon Stricker (1834-1898), who advocated a mixture of wax and oil; and Andrew Pritchard (1804-1884) who, in 1832, used a gum/isinglass mixture. In the same year, Canada balsam appeared on the scene, and in 1869 Edwin Klebs (1834-1913) reported that he had for some years embedded his specimens in paraffin.

The 1906 Nobel Prize in Physiology or Medicine was awarded to histologists Camillo Golgi and Santiago Ramon y Cajal. They had conflicting interpretations of the neural structure of the brain based on differing interpretations of the same images. Ramón y Cajal won the prize for his correct theory, and Golgi for the silver-staining technique that he invented to make it possible.

In vivo histology
Currently there is intense interest in developing techniques for in vivo histology (predominantly using MRI), which would enable doctors to non-invasively gather information about healthy and diseased tissues in living patients, rather than from fixed tissue samples.

title: Histology


text:
Henry VII

Henry VII may refer to:

 * Henry VII of England (1457–1509), King of England and Lord of Ireland from 1485 until his death in 1509; the founder of the House of Tudor
 * Henry VII, Duke of Bavaria (died 1047), count of Luxembourg (as Henry II) from 1026 and duke of Bavaria from 1042 until his death
 * Henry (VII) of Germany (1211–1242), King of Sicily from 1212, Duke of Swabia from 1216, and King of Germany from 1220
 * Henry VII, Holy Roman Emperor (c. 1273–1313), King of Germany from 1308 and Holy Roman Emperor from 1312
 * Henry VII, Count of Schwarzburg-Blankenburg (13th-century–1324), also known as Henry VI, the ruling Count of Schwarzburg-Blankenburg from 1285 until his death
 * Henry VII Rumpold (c. 1350–1395), Duke of Żagań-Głogów during 1368–1378 and ruler over half of Głogów, Ścinawa and Bytom Odrzański since 1378
 * Henry VII, Count of Waldeck (14th-century–15th-century), Count of Waldeck from 1397 until his death
 * Heinrich VII, Prince Reuss of Köstritz (1825–1906)
 * Henri, Count of Paris (1933–2019), Orléanist pretender to the defunct French throne as Henry VII

title: Henry VII


text:
Herodotus

Herodotus (c. 484 BC) was a Greek historian and geographer from the Greek city of Halicarnassus, part of the Persian Empire (now Bodrum, Turkey) and a later citizen of Thurii in modern Calabria, Italy. He is known for having written the Histories – a detailed account of the Greco-Persian Wars. Herodotus was the first writer to perform systematic investigation of historical events. He has been described as "The Father of History", a title conferred on him by the ancient Roman orator Cicero.

The Histories primarily cover the lives of prominent kings and famous battles such as Marathon, Thermopylae, Artemisium, Salamis, Plataea, and Mycale. His work deviates from the main topics to provide a cultural, ethnographical, geographical, and historiographical background that forms an essential part of the narrative and provides readers with a wellspring of additional information.

Herodotus was criticized in ancient times for his inclusion of "legends and fanciful accounts" in his work. The contemporaneous historian Thucydides accused him of making up stories for entertainment. However, Herodotus explained that he reported what he could see and was told. A sizable portion of the Histories has since been confirmed by modern historians and archaeologists.

Life
Modern scholars generally turn to Herodotus' own writing for reliable information about his life, supplemented with ancient yet much later sources, such as the Byzantine Suda, an 11th-century encyclopedia which possibly took its information from traditional accounts. Still, the challenge is great:

"The data are so few – they rest upon such late and slight authority; they are so improbable or so contradictory, that to compile them into a biography is like building a house of cards, which the first breath of criticism will blow to the ground. Still, certain points may be approximately fixed ..."

Childhood
Herodotus was, according to his own statement, at the beginning of his work, a native of Halicarnassus in Anatolia, and it is generally accepted that he was born there around 485 BC. The Suda says his family was influential, that he was the son of Lyxes and Dryo and the brother of Theodorus, and that he was also related to Panyassis – an epic poet of the time.

Halicarnassus was then within the Persian Empire, making Herodotus a Persian subject, and it may be that the young Herodotus heard local eyewitness accounts of events within the empire and of Persian preparations for the invasion of Greece, including the movements of the local fleet under the command of Artemisia I of Caria.

Inscriptions recently discovered at Halicarnassus indicate that Artemesia's grandson Lygdamis negotiated with a local assembly to settle disputes over seized property, which is consistent with a tyrant under pressure. His name is not mentioned later in the tribute list of the Athenian Delian League, indicating that there might well have been a successful uprising against him some time before 454 BC.

Herodotus wrote his Histories in the Ionian dialect, in spite of being born in a Dorian settlement. According to the Suda, Herodotus learned the Ionian dialect as a boy living on the island of Samos, to which he had fled with his family from the oppressions of Lygdamis, tyrant of Halicarnassus and grandson of Artemisia. Panyassis, the epic poet related to Herodotus, is reported to have taken part in a failed uprising.

The Suda also states that Herodotus later returned home to lead the revolt that eventually overthrew the tyrant. Due to recent discoveries of inscriptions at Halicarnassus dated to about Herodotus' time, it is now know that the Ionic dialect was used in Halicarnassus in some official documents, so there is no need to assume (like the Suda) that he must have learned the dialect elsewhere. The Suda is the only source placing Herodotus as the heroic liberator of his birthplace, casting doubt upon the veracity of that romantic account.

Early travels
As Herodotus himself reveals, Halicarnassus, though a Dorian city, had ended its close relations with its Dorian neighbours after an unseemly quarrel (I, 144), and it had helped pioneer Greek trade with Egypt (II, 178). It was, therefore, an outward-looking, international-minded port within the Persian Empire, and the historian's family could well have had contacts in other countries under Persian rule, facilitating his travels and his researches.

Herodotus' eyewitness accounts indicate that he traveled in Egypt in association with Athenians, probably sometime after 454 BC or possibly earlier, after an Athenian fleet had assisted the uprising against Persian rule in 460–454 BC. He probably traveled to Tyre next and then down the Euphrates to Babylon. For some reason, possibly associated with local politics, he subsequently found himself unpopular in Halicarnassus, and sometime around 447 BC, migrated to Periclean Athens – a city whose people and democratic institutions he openly admired (V, 78). Athens was also the place where he came to know the local topography (VI, 137; VIII, 52–55), as well as leading citizens such as the Alcmaeonids, a clan whose history is featured frequently in his writing.

According to Plutarch, Herodotus was granted a financial reward by the Athenian assembly in recognition of his work. Plutarch, using Diyllus as a source, says this was 10 talents.

Later life
In 443 BC or shortly afterwards, he migrated to Thurii, in modern Calabria, as part of an Athenian-sponsored colony. Aristotle refers to a version of the Histories written by "Herodotus of Thurium", and some passages in the Histories have been interpreted as proof that he wrote about Magna Graecia from personal experience there (IV, 15,99; VI, 127). Intimate knowledge of some events in the first years of the Peloponnesian War (VI, 91; VII, 133, 233; IX, 73) suggests that he returned to Athens, in which case it is possible that he died there during an outbreak of the plague. It is also possible he died in Macedonia instead, after obtaining the patronage of the court there; or else he died back in Thurii. There is nothing in the Histories that can be dated to later than 430 BC with any certainty, and it is generally assumed that he died not long afterwards, possibly before his sixtieth year.

Author and orator
Herodotus would have made his researches known to the larger world through oral recitations to a public crowd. John Marincola writes in his introduction to the Penguin edition of the Histories that there are certain identifiable pieces in the early books of Herodotus' work which could be labeled as "performance pieces". These portions of the research seem independent and "almost detachable", so that they might have been set aside by the author for the purposes of an oral performance. The intellectual matrix of the 5th century, Marincola suggests, comprised many oral performances in which philosophers would dramatically recite such detachable pieces of their work. The idea was to criticize previous arguments on a topic and emphatically and enthusiastically insert their own in order to win over the audience.

It was conventional in Herodotus' day for authors to "publish" their works by reciting them at popular festivals. According to Lucian, Herodotus took his finished work straight from Anatolia to the Olympic Games and read the entire Histories to the assembled spectators in one sitting, receiving rapturous applause at the end of it. According to a very different account by an ancient grammarian, Herodotus refused to begin reading his work at the festival of Olympia until some clouds offered him a bit of shade – by which time the assembly had dispersed. (Hence the proverbial expression "Herodotus and his shade" to describe someone who misses an opportunity through delay.) Herodotus' recitation at Olympia was a favourite theme among ancient writers, and there is another interesting variation on the story to be found in the Suda: that of Photius and Tzetzes, in which a young Thucydides happened to be in the assembly with his father, and burst into tears during the recital. Herodotus observed prophetically to the boy's father, "Your son's soul yearns for knowledge."

Eventually, Thucydides and Herodotus became close enough for both to be interred in Thucydides' tomb in Athens. Such at least was the opinion of Marcellinus in his Life of Thucydides. According to the Suda, he was buried in Macedonian Pella and in the agora in Thurii.

Place in history
Herodotus announced the purpose and scope of his work at the beginning of his Histories:

"Here are presented the results of the inquiry carried out by Herodotus of Halicarnassus. The purpose is to prevent the traces of human events from being erased by time, and to preserve the fame of the important and remarkable achievements produced by both Greeks and non-Greeks; among the matters covered is, in particular, the cause of the hostilities between Greeks and non-Greeks."

- Herodotus, The Histories (tr. R. Waterfield, 2008)

Predecessors
His record of the achievements of others was an achievement in itself, though the extent of it has been debated. Herodotus' place in history and his significance may be understood according to the traditions within which he worked. His work is the earliest Greek prose to have survived intact. However, Dionysius of Halicarnassus, a literary critic of Augustan Rome, listed seven predecessors of Herodotus, describing their works as simple, unadorned accounts of their own and other cities and people, Greek or foreign, including popular legends, sometimes melodramatic and naïve, often charming – all traits that can be found in the work of Herodotus himself.

Modern historians regard the chronology as uncertain, but according to the ancient account, these predecessors included Dionysius of Miletus, Charon of Lampsacus, Hellanicus of Lesbos, Xanthus of Lydia and, the best attested of them all, Hecataeus of Miletus. Of these, only fragments of Hecataeus' works survived, and the authenticity of these is debatable, but they provide a glimpse into the kind of tradition within which Herodotus wrote his own Histories.

Contemporary and modern critics
It is on account of the many strange stories and the folk-tales he reported that his critics have branded him "The Father of Lies". Even his own contemporaries found reason to scoff at his achievement. In fact, one modern scholar has wondered whether Herodotus left his home in Greek Anatolia, migrating westwards to Athens and beyond, because his own countrymen had ridiculed his work, a circumstance possibly hinted at in an epitaph said to have been dedicated to Herodotus at one of his three supposed resting places, Thuria:

Yet it was in Athens where his most formidable contemporary critics could be found. In 425 BC, which is about the time that Herodotus is thought by many scholars to have died, the Athenian comic dramatist Aristophanes created The Acharnians, in which he blames the Peloponnesian War on the abduction of some prostitutes – a mocking reference to Herodotus, who reported the Persians' account of their wars with Greece, beginning with the rapes of the mythical heroines Io, Europa, Medea, and Helen.

Similarly, the Athenian historian Thucydides dismissed Herodotus as a story-teller. Thucydides, who had been trained in rhetoric, became the model for subsequent prose-writers as an author who seeks to appear firmly in control of his material, whereas with his frequent digressions Herodotus appeared to minimize (or possibly disguise) his authorial control. Moreover, Thucydides developed a historical topic more in keeping with the Greek world-view: focused on the context of the polis or city-state. The interplay of civilizations was more relevant to Greeks living in Anatolia, such as Herodotus himself, for whom life within a foreign civilization was a recent memory.

Though Herodotus is generally considered a reliable source of ancient history, many present-day historians believe that his accounts are at least partially inaccurate, attributing the observed inconsistencies in the Histories to exaggeration.

Critical editions

 * C. Hude (ed.) Herodoti Historiae. Tomvs prior: Libros I–IV continens. (Oxford 1908)
 * C. Hude (ed.) Herodoti Historiae. Tomvs alter: Libri V–IX continens. (Oxford 1908)
 * H. B. Rosén (ed.) Herodoti Historiae. Vol. I: Libros I–IV continens. (Leipzig 1987)
 * H. B. Rosén (ed.) Herodoti Historiae. Vol. II: Libros V–IX continens indicibus criticis adiectis (Stuttgart 1997)
 * N. G. Wilson (ed.) Herodoti Historiae. Tomvs prior: Libros I–IV continens. (Oxford 2015)
 * N. G. Wilson (ed.) Herodoti Historiae. Tomvs alter: Libri V–IX continens. (Oxford 2015)

Translations
Several English translations of Herodotus' Histories are readily available in multiple editions. The most readily available are those translated by:
 * Henry Cary, translation 1849: text Internet Archive
 * George Rawlinson, translation 1858–1860. Public domain; many editions available, although Everyman's Library and Wordsworth Classics editions are the most common ones still in print. (revised in 1935 by A. W. Lawrence)
 * George Campbell Macaulay, translation 1890, published in two volumes. London: Macmillan and Co.
 * A. D. Godley 1920; revised 1926. Reprinted 1931, 1946, 1960, 1966, 1975, 1981, 1990, 1996, 1999, 2004. Available in four volumes from Loeb Classical Library, Harvard University Press. ISBN 0-674-99130-3 Printed with Greek on the left and English on the right:
 * A. D. Godley Herodotus : The Persian Wars : Volume I : Books 1–2 (Cambridge, Massachusetts 1920)
 * A. D. Godley Herodotus : The Persian Wars : Volume II : Books 3–4 (Cambridge, Massachusetts 1921)
 * A. D. Godley Herodotus : The Persian Wars : Volume III : Books 5–7 (Cambridge, Massachusetts 1922)
 * A. D. Godley Herodotus : The Persian Wars : Volume IV : Books 8–9 (Cambridge, Massachusetts 1925)
 * Aubrey de Sélincourt, originally 1954; revised by John Marincola in 1996. Several editions from Penguin Books available.
 * David Grene, Chicago: University of Chicago Press, 1985.
 * Robin Waterfield, with an Introduction and Notes by Carolyn Dewald, Oxford World Classics, 1997. ISBN 978-0-19-953566-8
 * Andrea L. Purvis, The Landmark Herodotus, edited by Robert B. Strassler. Pantheon, 2007. ISBN 978-0-375-42109-9 with adequate ancillary information.
 * Walter Blanco, Herodotus: The Histories: The Complete Translation, Backgrounds, Commentaries. Edited by Jennifer Tolbert Roberts. New York: W. W. Norton, 2013.
 * Tom Holland, The Histories, Herodotus. Introduction and notes by Paul Cartledge. New York, Penguin, 2013.

title: Herodotus