Thomas Hausberger
email: thomas.hausberger@umontpellier.fr

A workshop on the epistemology and didactics of mathematical structuralism

Keywords: mathematical structuralism, Abstract Algebra, Group Theory, Anthropological Theory of the Didactic, structuralist praxeology, dialectic of objects and structures

This workshop was dedicated to a discussion of epistemological and didactic aspects of mathematical structuralism with a focus on Abstract Algebra, in particular Group Theory. The participants worked on a corpus of documents comprising excerpts of the Bourbaki Manifesto "the architecture of mathematics" and the transcript of a discussion thread from a mathematical forum online. To what extent does mathematical structuralism rely on didactic principles? How is this reflected in a teaching-learning environment? The key construct within the Anthropological Theory of the Didactic was the theoretical notion of "structuralist praxeology", introduced by the author. The analyses of the corpus led to the discussion of the rationale of such praxeologies, their historical development, how they may be reconstructed by learners, and the role played by the "dialectic of objects and structures" that should be added to Chevallard's model for study and research processes in order to account for the development of structuralist praxeologies.

Epistemology of mathematical structuralism

Mathematical structuralism takes its roots in the re-foundation of algebra operated by German algebraists at the beginning of the 20th Century. Workshop participants were thus given a few historical landmarks on the emergence of the group, ring and field structures, following [START_REF] Wussing | The Genesis of the Abstract Group Concept[END_REF] and [START_REF] Corry | Modern algebra and the rise of mathematical structures[END_REF]. Synthetic accounts may be found in (Hausberger, 2018b).

The idea of algebraic structures as a unifying principle is due to Noether: in the 1920s, she got Abstract Algebra away from thinking about operations on elements (such as addition or multiplication in groups or rings) but described structures in terms of selected subsets (such as normal subgroups of groups or ideals in Ring Theory) and homomorphisms. Noether and her school thus changed the way theorems were proved in algebra, focusing on general proofs that limit the calculations and put to the fore the "most general and fundamental" (hence simpler, according to structuralist views) concepts. This mathematical re-foundation of algebra also paved the way for unprecedented mathematical constructs, such as noetherian rings.

The structuralist method is well described in the [START_REF] Bourbaki | The architecture of mathematics[END_REF] Manifesto, entitled "the architecture of mathematics", written by a group of French mathematicians who were the great promoters of structuralist thinking. Indeed, Bourbaki set out to apply the method developed by the German algebraists to all fields of mathematics. The first part of the workshop was dedicated to the discussion of excerpts of the Manifesto. Bourbaki describes the structuralist use of the axiomatic method both as a method of exposition of mathematical theories and a method of discovery of new results (thus a heuristic). He draws conclusions on the impact of structuralism on mathematical activity and the organization of mathematical theories.

The starting point of the workshop was a couple of remarks that guided the reading of the Manifesto. Firstly, Bourbaki is aiming at the "profound intelligibility" of mathematics through the axiomatic method which "teaches us to look for the deep-lying reasons for such a discovery, to find the common ideas of these theories, buried under the accumulation of details properly belonging to each of them, to bring these ideas forward and to put them in their proper light". This suggests that didactic principles are governing Bourbaki's reconstruction of mathematical knowledge. Secondly, Bourbaki sees structures as "tools for the mathematician"; he emphasizes the "standardization of mathematical techniques" by means of the axiomatic method which is "nothing but the Taylor system for mathematics". This connects to the praxeological point of view of the Anthropological Theory of Didactic (ATD) which sees mathematical activity as the development of combinations of praxis and logos (praxeologies, Chevallard 2006). The following questions were thus discussed: 1. Which statements of the Bourbaki discourse express didactic concerns? To what extent does mathematical structuralism rely (or not) on didactic principles as a method of exposition and a method of discovery? How to phrase these principles in terms of didactics of mathematics? 2. Using the vocabulary of ATD, how to describe the impact of structuralism on mathematical praxeologies, in particular the praxis and logos blocks, the interrelations of both, on mathematical organizations in general?

Participants underlined that the writing of the Manifesto is itself a didactic gesture: in order to disseminate mathematics (Bourbaki wrote a treatise in several volumes: Elements de mathématiques), one must have a clear vision of what mathematics is. As pointed out in the Manifesto, "[it is] out of the question to give to the uninitiated an exact picture of that which the mathematicians themselves can not conceive in its totality". This quote refers to a stage of development of mathematics in which diversity hindered the production, communication and dissemination of mathematics. This is where the structuralist method comes into play as a didactic method to promote understanding and sense-making through "separating out the principal mainsprings of the arguments; then taking each of them separately and formulating it in abstract forms, to develop the consequences which follow from it alone". Bourbaki also refers to an "economy of thought", which may be related to the economy of didactic memory. Nevertheless, setting out abstraction and generality as principles was also debated among workshop participants (as among mathematicians, for instance Mandelbrot who discussed relationships between explanation, generality and abstraction). At first sight, a few educators -perhaps those who least share the Bourbaki culture -exclaimed: "Don't do that!" (the use of such principles in classrooms).

In fact, Bourbaki describes and justifies in the Manifesto techniques to solve problems and to write and communicate mathematical theories. In other words, all the elements of mathematical research praxeologies may be found. Readers may draw a list of structuralist techniques to solve problems: "to recognize among the elements relations which satisfy axioms of known types", "to apply the arsenal of general theorems which belong to the structure of that type", "to orient the intuitive course of one's thought [according to the structural insights]"; and structuralist techniques for the exposition of mathematics: "to look for deep-lying reasons", "to find common ideas of theories and bring them forward", "to separate out the mainsprings of its arguments", "to inquire how these different components influence each-other", "to set up the axiomatic theory of a given structure".

The phenomena of unification of punctual praxeologies into regional and global praxeologies was related by several participants to the Bourbaki discourse of unification of mathematics under the axiomatic method. The holistic vision of Bourbaki was questioned as an epistemological point of view that may be relativised (it applies to algebra but maybe not with the same pertinence to every mathematical domain) and as a socio-cultural norm. Participants pointed out that distinctions should be made between mathematical praxeologies in teaching institutions (including universities), in research institutions (also including universities), and in different fields or domains, considering also variations between societies and civilisations (in reference to the scale of levels of didactic codeterminacy). Nevertheless, it was argued that some common points (consistent with the Bourbaki discourse) may be found: privileging the "most general formulations" (of theorems, definitions, etc.); the role played by Theory to unify mathematical sectors and domains (regional praxeologies); a further Metatheory to unify the discipline in a global praxeology. Other participants underlined that the structuralist method induced changes at the discipline level, for instance the creation of new domains and sectors (general set-theoretic topology, algebraic topology,…). It was accompanied by important modifications in the praxis (and of course logos), as new questions appeared and new ways of proving results (new techniques). At this stage of the workshop, the need of new tools emerged to make such statements more precise.

Modeling mathematical structuralism within ATD

The notion of structuralist praxeology (Hausberger, 2018a) aims at modeling within ATD the epistemological ideas developed above. Structuralist thinking is characterised by reasoning in terms of classes of objects, relationships between these classes and stability of properties under operations on structures. The application of the structuralist method relies on a dialectic between the particular and the general, or in other words between objects and structures. The questions and problems are raised to a higher level of generality in order to apply structuralist concepts (e.g., ideal, principal ideal domain, etc.) and tools (e.g., isomorphism theorems, structure theorems, combinatorial of structures, etc.) according to the moto "generalizing is simplifying". In other words, the "structuralist methodology aims at replacing a praxeology [T, ?, ?, Θ particular ] by a structuralist praxeology [T g , τ, θ, Θ general ], where T g is a generalization of T that allows the use of structuralist techniques" (loc. cit. p. 83). In order to illustrate the theoretical construct of structuralist praxeology, workshop participants were presented the example of the thread on decimal numbers from the online forum mathematiques.net (loc. cit. pp.83-87). To prove that the ring D of decimals is a principal ideal domain, the forum students searched for a proof of the general statement that any subring of Q is principal, then investigated whether principality was transferred from a ring to its subrings. The study of these dialogues emphasise the role of the dialectic of objects and structures in the development of structuralist praxeologies: structures are applied as a generalizing-simplifying viewpoint in order to demonstrate properties on mathematical objects and, conversely, a semantic control of the formal general statements on structures is exercised by putting them to the test of known examples

(Q[x] is principal but Z[X] is not).
Inspired by [START_REF] Winsløw | Transformer la théorie en tâches : la transition du concret à l'abstrait en analyze réelle[END_REF] praxeological formalisation of the concrete to abstract transition in analysis (from calculus to more theoretical tasks involving continuity and differentiability of functions as well as the topology of real numbers), the author proposed a model for the epistemological transition to Abstract Algebra, in two phases: the first phase is concerned with the transition from T to T g described above and leads to the construction of a structuralist praxeology as a fertile strategy to prove properties of concrete objects; the second phase builds on structuralist praxeologies previously developed in order to introduce more abstract and theoretical types of tasks that only consider classes of objects with their structural properties (e.g.: show that a Noetherian integral domain such that every maximal ideal is principal is a principal ideal domain).

A new example related to arithmetic and abelian Group Theory (GT) was then introduced at the workshop. Indeed, Bourbaki cautiously explained that his account of structuralism is a schematic and idealized sketch, and so is the model described above. Its pertinence in the elucidation of teaching-learning phenomena related to GT needs be investigated through concrete case studies. The case of GT was also chosen to relate to other didactic studies. For instance, [START_REF] Bosch | Questioning Mathematical Knowledge in Different Didactic Paradigms: the Case of Group Theory[END_REF] focused "not only on the official raison d'être of GT within university teaching, but also on different possible alternative ones that could motivate or impel the use of GT to solve problematic questions". In particular, they looked for external problems (that is, external to GT) that could lead to the reproduction of a substantial part of GT as a means to ascribe some rational to it. Precisely, they argued that a counting problem (such as that of symmetries of a square) may be a suitable candidate for a reconstruction of elementary GT. This choice is justified by the links between GT and the notions of symmetry and invariant in the historical development of GT and by the role played by Lagrange's theorem as a tool to solve the problem. Nevertheless, it also raises epistemological issues: for instance, "is it substantial enough to motivate the study of the isomorphism theorems"?

The problem discussed at the workshop is classical, external to GT, and may be found in standard textbooks [START_REF] Perrin | Cours d'algèbre[END_REF]: determine the set of primes p such that -1 is a quadratic residue (congruent to a perfect square) modulo p. Such questions follow from the work of number theorists of the 17 th and 18 th centuries (Fermat, Euler, Lagrange, Legendre) and have been given a first systematic treatment in Gauss's Disquisitiones Arithmeticae ( 1801). The answer to this question is called "first supplement to the law of quadratic reciprocity" (p = 2 or p ≡ 1 (mod 4)). The ambition is not to cover a substantial part of GT but simply illustrate the structuralist methodology.

The problem may be considered inside arithmetic as a particular theory (in the sense of Bourbaki) in dialectical relationship with GT (through the group (Z/pZ)*), Field Theory (F p ), or even Ring Theory (Z[i], F p [X]) as general structures. Students may stay in arithmetic (as a theory in the sense of ATD), use Fermat's little theorem to prove that (-1) (p-1)/2 ≡ 1 (mod p) and deduce the necessity of the condition p ≡ 1 (mod 4). The converse implication is less straightforward (the reader may have a try or look up Gauss's DA art 111), but gains much clarity when translated into structural terms. Indeed, the set Q of quadratic residues modulo p make up a subgroup of index 2 in F p * (as the image of the homomorphism x↦x 2 ). It thus contains (p-1)/2 elements (and we may recover the preceding result by means of Lagrange's theorem). Moreover, the equation x (p-1)/2 =1 in F p admits at most (p-1)/2 solutions since F p is a field. This proves that the set of solutions is exactly Q and the result follows. Another proof uses the argument that a group of even order always possesses an element of order 2 (a well-known result in elementary GT) to conclude that -1 belongs to Q (under the hypothesis p ≡ 1 (mod 4)), since it is the unique element of order 2. The problem may thus be related to standard praxeologies from GT (show that a subset is a group, determine its order and use known results on orders of elements) or mixed arguments using a property of polynomials defined over a field.

In this example, the type of task T (find conditions for the existence of a solution of a congruence) is handled with respect to the structural properties of the given congruence equation, and thus gives birth to the structuralist types of tasks (which are not direct generalizations of T), once structures are identified. The first isomorphism theorem, Lagrange's theorem and other general results about groups play the role of technologies. Theories of structures (GT, abelian GT, FT, RT) orient the work and provide the (formalized part of the) theory in the sense of ATD.

The thread on (Z/32Z)* and abelian Group Theory

Although many mathematical problems from GT may be stated independently on GT as we have just seen, the concepts of GT often offer an adequate framework to state GT problems in a synthetic meaningful way, as well as inspiring new problems as further natural developments. Looking up at lists of problems collected and proposed by mathematicians to students, for instance https://yutsumura.com/welcome-to-problems-in-mathematics/, it is striking that the structuralist scope is put in the fore to give a title to the problems (Prove a Group is Abelian if ( a b ) 2 = a 2 b 2 Quotient Group of Abelian Group is Abelian A Group is Abelian if and only if Squaring is a Group Homomorphism). Therefore, the success of students to solve these problems very much depend on their ability to connect the statements to the core structuralist praxeologies that they previously met, in other words their structuralist praxeological equipment and their understanding of the structuralist methodology.

For the last part of the workshop, participants focused on a problem that was submitted by a student (ianchenmu) to the Math Help Board (MHB) forum. MHB presents itself as an "online community that gives free mathematics help any time of the day about any problem, no matter what the level". As stated by ianchenmu, "the question is to identify isomorphism type for each proper subgroup of (Z/32Z) × ". The student wonders about the meaning of "isomorphism type", guesses that isomorphisms need to be found between each such subgroup and "another group" and questions about the method to proceed. A math scholar and MHB moderator (Klaas_van_Aarsen) helps ianchenmu to advance through the task, and another student (jakncoke) joins in to share his views. The thread may be accessed via this link 1 and a transcript of the collective study process was provided at the workshop.

The study process may be modeled by a study and research path (SRP; [START_REF] Chevallard | Steps toward a new epistemology in mathematics education[END_REF] as the author did for the thread on decimal numbers (Hausberger, 2018a;[START_REF] Hausberger | Enseignement et apprentissage de l'algèbre abstraite à l'Université : vers un paradigme du questionnement du monde[END_REF]. The chronogenesis is governed by a dialectic between questions and answers while the mesogenesis involves a dialectic of medias and milieus [START_REF] Chevallard | Un concept en émergence : la dialectique des médias et des milieux[END_REF]. Special attention should be paid to the mathematical praxeologies that are developed through the SRP, in particular structuralist praxeologies that, as we have seen, usually appear through the dialectic of objects and structures.

The following questions were proposed for discussion at the workshop: 1. Do you have any idea about the historical origin of such a problem? To which sector and theme of the Abstract Algebra curriculum would you connect this problem to? 2. What are the main praxeologies developed during the study process online? 3. Which structuralist aspects can you identify? What are the objects and structures involved? Can you observe a dialectic between objects and structures? 4. What is your evaluation of the dialectic of medias and milieus, and the global vitality of the study process? 5. What are, according to you, the main conditions that hinder/foster the development of structuralist praxeologies (the ecological question)? If you were moderating the forum, what strategy would you adopt to "link problem solving and learning content" and thus address the "challenges of self-sustained study and research processes" [START_REF] Bosch | Linking problem solving and learning content: the challenges of self-sustained study and research processes[END_REF]? What would you retain from Bourbaki's didactic principles? Answers or partial answers to these questions are proposed and discussed in the sequel.

Considering the formulation of the problem by ianchenmu, two types of tasks emerge: determine the lattice of subgroups of a given finite abelian group G (T 1 ), determine the isomorphism type (or structure) of a given finite abelian group (T 2 ). The type of tasks T 2 must be understood in relation to the fundamental theorem of finite abelian groups (FTAG), which clarifies the notion of "type": every finite abelian group can be expressed as the direct sum of cyclic subgroups of prime-power order. According to [START_REF] Wussing | The Genesis of the Abstract Group Concept[END_REF], the FTAG, was proven by Kronecker in 1870, using a grouptheoretic proof, though without stating it in group-theoretic terms. This generalised an earlier result of Gauss from Disquitiones Arithmeticae (1801), which classified quadratic forms. The theorem was stated and proved in the language of groups by Frobenius and Stickelberger in 1878.

The type of tasks T 1 and type of group G = (Z/nZ) × both take roots in Galois Theory (GT). Indeed, such groups are the Galois groups of cyclotomic field extensions (generated over Q by a primitive n-th root of unity), and GT states a correspondence between the lattice of field extensions and the lattice of subgroups (the latter being easier to determine). Finally, the isomorphism types of (Z/nZ) × are known: by the Chinese remainder theorem, it is enough to determine the type in the case n is a primer power p r ; moreover, (Z/p r Z) × is cyclic except in the case p = 2 and r ≥ 2 in which (Z/2 r Z) × ≃ Z/2 r-2 Z × Z/2 Z. The parameters p and r (= 5) are thus important didactic variables.

There are introductory as well as advanced textbooks on GT, covering GT or Abstract Algebra in general. The lattice of subgroups is often not a topic covered by elementary textbooks, the classification of groups according to isomorphism types being the culmination of the course. In [START_REF] Dummit | Abstract Algebra[END_REF], a more advanced textbook, the lattice of subgroups appears as a topic of chapter 2 "subgroups" (the theme) within part 1 GT (sector). The FTAG (generalised to finitely generated abelian groups) and the classification problem are presented in chapter 5 on "direct and semidirect products and abelian groups".

Several techniques are developed on the forum to solve the main types of tasks T 1 and T 2 . Regarding the former: τ 1,Klass : determine cyclic subgroups; if g does not generate G, add other elements; τ 1,ianchenmu : compute <g> for all g in G ["it's so much work"];τ 1a,Jakncoke : if G = Z/nZ, use the fundamental theorem of cyclic groups; τ 1b,Jakncoke : determine the possible orders of subgroups thanks to Lagrange's theorem and the possible isomorphism types thanks to the FTAG. Then construct subgroups by looking at orders of elements and then combining elements by means of direct products [erroneous part of the technique]. The technology includes the definition of a cyclic group, Lagrange's theorem and the fundamental theorems (used implicitly by Jakncoke). Regarding the latter: τ 2a,Klass : if G is cyclic of order n, then the isomorphism type is that of Z/nZ; τ 2b,Klass : give all possible isomorphism types thanks to the FTAG and conclude by examining orders of elements; τ 2,ianchenmu : if G = < a, b, c > then the isomorphism type is that of the direct product of cyclic groups of orders given by those of the 3 generators [erroneous technique]. The technology here includes the definitions of the isomorphism type and cartesian product, and the FTAG. In fact, three related auxiliary types of tasks are discussed on the forum: T 3 : determine the order of an element g in G; T 4 : determine the list of elements of an abelian group G = < a, b >; T 5 : show that a given group of order 4 is isomorphic to the Klein group V 4 .

Several structuralist aspects of the problem may be pointed out: 1. at the level of mathematical concepts, the problem involves: the mathematical structures of group and the partial order < on subgroups; the notion of isomorphism type (abstract structure of a group); the lattice of subgroups that "encodes" part of the group-theoretic information. 2. at the level of methods, the following structuralist principles are encountered: thinking in terms of generators (and relations); thinking up to isomorphism (isomorphisms preserve "structural information"); to decompose into simple components (structure theorems); to combine simple components (direct product).

Let us now focus on the dialectic of objets and structures. The main objects met during the study process are the groups Z/32Z and (Z/32Z) × , and instances of products of cyclic groups (e.g. V 4 ).

The main structures are < a, b > (abstract group on generators) and ∏ Z / p i r i Z (FTAG), which serve as abstract models. The dialectical aspects may be described as follows: the structures serve as tools to determine subgroups of (Z/32Z) × (by means of generators) and their isomorphism types (τ 2,ianchenmu ; the fundamental theorem as a means to predict possible models). Respectively, further elements of the logos on structures emerged (but only implicity) to fulfill technical needs: the implicit erroneous formulas <a, b> = <a> < ∪ b> and <a,b,c> ≃ Z/o(a) Z×Z/o(b)Z×Z/o(c) Z, which were refuted during the study process. Unfortunately, conditions for such a isomorphism to hold (in the simplest case of 2 elements) were not discussed, as well as more advanced structuralist questions such as the behavior of the lattice of subgroups under direct product of groups.

Let us now conclude on the ecology of structuralist praxeologies. Our analysis shows that the study process evolved towards more and more basic praxeologies (T 4 , T 5 ) due to a lack in the praxeological equipment of ianchenmu that hindered the possibility to deal with the main tasks. Moreover, the moderator only focused on ianchenmu and didn't help jakncoke develop more advanced praxeologies. The dialectic of medias and milieus is very limited (very few elements of the medias were brought up in the milieu and no media on lattice of subgroups was identified): one hypothesis is that ianchenmu lacked skills to identify pertinent sources and therefore relied on Klauss who played the role of teacher. The dialectic of objects and structures is also limited: structures were applied as tools but techniques did not lead to further theoretical developments (new general results about structures to test on known examples). The two types of tasks T 1 and T 2 were not related as they could (role of information on the structure of G to construct its lattice of subgroups), and the structuralist methods were not supported by structuralist insights as a metadiscourse (a technology): e.g. the notion of isomorphism type was not clarified by Klauss.

Finally, if the FTAG illuminates the role of cyclic groups, it hinders the work on constructing isomorphisms "by hand" to link <a,b> and Z/o(a) Z×Z/o(b)Z (the issue of the economy of techniques). In [START_REF] Dummit | Abstract Algebra[END_REF], the task T 1 on lattice of subgroups is discussed three chapters before the FTAG (generalised) is taught. This suggests, by contrast with structuralist principles, that it would be preferable to separate the two types of tasks, at an early stage of the development of structuralist praxeologies in GT.

https://mathhelpboards.com/linear-abstract-algebra-14/identify-isomorphism-type-each-propersubgroup-z-32z-3585.html


Filippo Furri
email: furrif@gmail.com

Ed B Banerjee

T Lacroix

J Misrahi-Barak

Towards a New Kinship? Affective Engagements with Migrants Dead in the Mediterranean Carolina Kobelinsky and

Keywords: ethnography of EU borders, identification of unknown migrants, affective engagement with the dead, kinship, hospitality

was one of the main arrival points for border crossers trying to reach the European Union without the necessary authorisation from nationstates. A small group of locals involved with the Red Cross in migrant reception in the port decided in 2017 to organise themselves in order to find a way of "respecting" the dead border crossers arriving on European territory, alongside the living, during the search and rescue operations that have formed part of the landscape around the Mediterranean for several years. The idea of respecting the deceased turned into a project to develop a database aimed at providing a name and a biography for the unknown bodies buried in the local cemetery. The team succeeded in convincing the institutions involved in dealing with these bodies of the value of cooperating, which enabled them to consult the files held about the deceased by various police agencies and municipal institutions.

Drawing on ethnographic material, we explore here an unexpected effect of the project. Our interlocutors -Red Cross volunteers, employees of the civil registry office, undertakers, forensic police officerswho were all involved in constructing the database, and more broadly in dealing with the bodies, soon expressed an attachment to the deceased. In this paper, we aim to examine the social and emotional feelings of connectedness that are created through everyday acts, and sometimes quite trivial actions: visiting the dead in the cemetery, naming them, dreaming of them recurrently, or telling stories about them during family gatherings. Combining an ethnographic account of these relationships with anthropological scholarship on kinship, as well as on death studies, we intend to bring out some of the features of the new place created within Catania, and among some of its inhabitants, for border crossers who have died at sea.

We treat them like any other body, but we can't lie, they affect us a lot… just as we're affected by the death of a young person here in an accident. When we receive someone who reports the death of a child, I feel it like a blow to the heart. When we're dealing with children here… or young people… An old man, well, it depends how he dies, if he's all alone, yes, of course that affects us too […] The migrants… they're young and they're alone, it touches all of us here. These dead, li portiamo a casa [we bring them home with us]. (Mr Mancini, 2 October 2019) This is how Mr Mancini, in charge of the municipal funeral service at the Catania cemetery, sums up the particular nature of the relationship with the dead border crossers who are brought to the city's port as part of search and rescue operations at sea. The funeral service, like the cemetery, but also the civil registry office, the police forensics department, and the squadra mobile (a division of the national police service tasked with criminal investigations), are all institutions accustomed to dealing with dead bodies. But, as this extract of a conversation with Mr Mancini illustrates, the bodies of people who have died in the Mediterranean while trying to reach Europe without the necessary authorisation from the various nation-states do not leave those who have to deal with them unmoved. On the contrary.

During the 2010s the city of Catania had to take care of hundreds of bodies. Most of these bodies were not only those of foreigners, but were also of unknown identity. The shipwreck that occurred in the Mediterranean on May 2014, which claimed the lives of seventeen people, whose remains were brought ashore in this city of 311,000 inhabitants in eastern Sicily, prompted the City Council to build a monument within the cemetery to physically accommodate them and pay tribute to them. The monument, named "Speranza naufragata" (wrecked hope), consists of seventeen tombstones on which are inscribed the lines of the poem "Migrations" by the Nigerian writer Wole Soyinka. In the centre, a sculpture represents a man standing above the waves, supported by external pillars. Only a few meters away, a space was made available in 2015 in order to bury the bodies of border crossers who arrived as a result of search and rescue operations at sea. 1 This space is arranged as a uniform square, with rows of small mounds of earth, on each of which a black metal plaque is fixed on the ground. Each plaque features a code, a date, and the name of a boat, which remind passers-by that these are people of whom we know nothing except that they came from elsewhere. 2 Whether they were buried in the "migrants' square" or within the monument, all these bodies arrived in Catania as a result of operations at sea between 2014 and 2018. They were brought ashore together with the men, women, and children who had survived the difficult conditions of travel on makeshift boats departing from Africa, mostly starting their crossing from Libyan coastal towns. On each occasion when the boats arrived at the port, different branches of the police, departments of the Ministry of the Interior and Ministry of Health, and associations were involved in the process of taking responsibility for them. For the living, the local Red Cross Committee provide first aid, water, biscuits, hygiene kits, and clothes. This is the first in a long series of exchanges between the migrants and representatives of many institutions 1 Operation "Mare Nostrum" was set up by Italy following a shipwreck off Lampedusa in October 2013, in which 356 people lost their lives. It was replaced in November 2014 by Operation "Triton", this time coordinated by Frontex, the EU's border and coastguard agency, but unlike its predecessor, its top priority is border surveillance rather than life-saving. 2 This space was initially set up to accommodate the first bodies to arrive in Catania following the shipwreck on 18 April 2015, but it was later used to accommodate all the bodies of migrants that were brought ashore at this port following search and rescue operations. The administration soon named this space the "quadrato migranti" (migrants' square). This is how all our interlocutors refer to this space.

with an on-site presence. Between 2015 and 2018 Catania was one of the foremost entry ports on Italian territory, and in March 2016 the city's port officially became a "hotspot", that is, an area that, in the words of the European Commission, is experiencing "extraordinary migratory pressure". As a result of this designation, a national system was set up to identify and register all the migrants who enter the country, and then to direct them to various structures throughout Italy, depending on the circumstances (for example, if they can apply for asylum, or benefit from special protection, or must be deported from the country) [START_REF] Tazzioli | Containment beyond Detention: The Hotspot System and Disrupted Migration Movements across Europe[END_REF]. Several thousand people whose lives were in danger at sea were brought ashore at Catania. Alongside these living people, many others did not survive the crossing. It is difficult to calculate the number of dead who remain somewhere at the bottom of the sea. The latest figureswhich are always underestimatedput the number of dead and missing at 22.849 between 2014 and November 2021. 3 During this period, more than 260 bodies brought ashore at Catania would come to be buried in the municipal cemetery.

The care for the dead is less standardised than the care for the living. It depends on the number of bodies found, but also on the skills and means available to the municipality where they arrive, whatever its financial situation may be. The city of Catania thus found itself having to materially manage these dead. Their presence is announced to institutions before they arrive at the port, allowing the municipal funeral servicewhere Mr Mancini works, whose words were quoted aboveto prepare its equipment and head for the port. This also allows the deputy public prosecutor to appoint one or more forensic doctors to attend the scene to carry out the external examination of the bodies, in order to determine the cause of death. The bodies are then taken to the morgue of one of the city's hospitals for DNA sampling and forensic inspection, which provides information on the physical characteristics of the deceased and any distinctive features (tattoos, piercings, dental condition, long-standing injuries, etc.). The objects and clothes found with the bodies are then catalogued before being sent for storage in the offices of the public prosecutor. Once all the information has been collected, the bodies are transported, within a variable timeframe (depending on the diligence of the various institutions), to the cemetery for burial in the "migrants' square".

In the meantime, a judicial investigation is launched to determine whether this particular death is the result of a crime and, if so, to find those responsible. In concrete terms, the investigation aims to track down the people-smugglers, who are omnipresent figures in the public discourse on migration issues, commonly accused, if not of killing migrants, at least of endangering lives by putting too many people on board dilapidated boats. 4 In this context, the public prosecutor may request an autopsy and carry out investigations to identify the victim. The autopsy is used to determine the cause of death, but for deaths at sea, the external examination conducted in the port is usually sufficient. Investigations aimed at identifying these bodies are non-existent, since no institution has among its missions the identification of these dead arriving from elsewhere.5 This is an astonishing contrast if we consider the many procedures of identification and traceability that are implemented for those who arrive alive on European territory.

In this paper we wish to explore the consequences of a unique initiative, set up by a small group of volunteers from the Red Cross of Catania who were involved in the disembarkations, which aimed to "respect" the dead border crossers arriving in the city, at the same time as assisting the living. An uneasiness, and even a form of anger about the absence of investigations aimed at identifying and returning the remains to the families, led these volunteers to conceive of a project to take care of the dead. This paper charts the developments and some of the effects of this project. For this we have drawn on ethnographic material collected in Catania. The will to "respect" the dead was already present when Filippo Furri first went to Catania and met some Red Cross volunteers in 2016. Through their discussions, and in interaction with his activism as part of the Boat4People coalition,6 the idea of a more formal project emerged. Filippo talked about it to Carolina Kobelinsky, who was already working on the treatment of the dead but on the Spanish border, and together they expressed their interest in and enthusiasm for the project. For their part, the Catania team felt that support from researchers would be an asset that could be foregrounded with institutional partners. Our agendas therefore converged and the field research was then co-designed with our initial interlocutors. During numerous stays in Catania between 2018 and 2021, we combined the classic work of observation and discussion with active support for the project, by participating in sessions for gathering information about the bodies and in meetings for reflecting on the possibilities of identification that were provided by these data. 7In the first section we briefly describe the origin of this initiative, as well as the institutional framework on which it was based. This will make it possible to highlight the importance of the concept of family for the people at the heart of the project. We then turn to the ways in which the dead enter into the lives of the people involved in the project, outside of the work space associated with the project itself. We will examine how the dead haunt our interlocutors and enter into their homes. Through more or less everyday practices, a new affiliation with the dead emerges, involving relationships which seem to us to be close to the realm of kinship. In the third section of the paper we draw on the anthropological literature on kinship and, in particular, on the ties of this kind that can be established between the living and the dead, in order to better understand the connectedness that our interlocutors have with these dead. We take up the link made by some scholars between kinship and hospitality, proposing to consider the ties at work in Catania as a form of hospitality leading to the emergence of kinship-type relationships. We also show how these new ties reflect a new "distribution of the sensible" [START_REF] Rancière | The Politics of Aesthetics. The Distribution of the Sensible[END_REF]). The last section raises the issue of the future of these relationships in the event that the dead are identified and hospitality comes to an end. And it concludes addressing another question, that of the more general transformative potential of these new ties with unknown dead migrants.

Caring for the family

The "progetto sulle salme" ["project on the dead"] or "la banca dati" ["the database"]as all our interlocutors call itwas set up in 2017, at a time when the frequency of arrivals at the port was becoming less intense. At the beginning, it involved only three motivated volunteers from the local Red Cross: Silvia, Riccardo, and Davide. All of them were actively involved in the RFL (Restoring Family Links) programme. RFL emerged decades ago within the international Red Cross and Red Crescent movement with the aim of helping families searching for loved ones missing as a result of armed conflicts or natural disasters, but it is now largely devoted to helping to restore contact between family members that has been lost owing to the conditions of crossing borders without the necessary authorisation from the various nation-states. At disembarkations, RFL volunteers distribute cards to let people newly arrived on European territory know that the programme can help them in case of family separation.

It is undoubtedly no coincidence that volunteers who are particularly involved in this programme, which is based on the importance of maintaining links within families, are concerned about these deaths "that the families cannot mourn", to use a phrase that we heard repeatedly from the three initiators of the project. Although the concept of family is not the subject of a precise legal framework in the texts in which the RFL programme is embedded, and our interlocutors do not dwell on what they mean by "family", it seems to us that their use of this term corresponds to the definition proposed in the Commentary on the Additional Protocols of 8 June 1977 to the Geneva Conventions of 12 August 1949, which lie at the heart of international humanitarian law:

In the narrow sense, the family covers persons related by blood and living together as one household. In a wider sense it covers all persons with the same ancestry. In the context of [this article] it would be wrong to opt for an excessively rigid or precise definition; common sense must prevail. Thus the word "family" here of course covers relatives in a direct linewhether their relationship is legal or naturalspouses, brothers and sisters, uncles, aunts, nephews and nieces, but also less closely related relatives, or even unrelated persons, belonging to it because of a shared life or emotional ties (cohabitation, engaged couples etc.). In short, all those who consider themselves and are considered by each other, to be part of a family, and who wish to live together, are deemed to belong to that family. (Commentary on the Additional Protocols of 8 June 1977 to the Geneva Conventions of 12 August 1949, Geneva, ICRC, 1986, p. 859) In one of our first in-depth conversations about the project, Silvia told us that one of her main goals to achieve was "that their family, parents, children, partners… that they know, that they're not in limbo, that the uncertainty stops". Besides her definition of family, it is also interesting to note that she puts herself in the position of those who have no news of a loved one. She imagines herself in the place of families. This was also the attitude adopted by Riccardo, Davide, and most of the interlocutors participating in the project from the various institutions involved.

We will return to the implications of this perspective. For now, let us go back to the story of how the project was set up. At a time when there was less activity in the port, a small team was formed among the RFL volunteers. With the agreement of the president of the local Red Cross Committee, they decided to start by mapping the graves in the municipal cemetery of migrants who had died in the Mediterranean. This allowed them to know the number of bodies buried and to gather together the information that was available at the time of burial. The team soon realised that if the aim was to work on identifying the bodies, it was necessary to set up an enquiry to retrace the migratory journey, leading back from the burial site to their families, wherever they might be.

The mapping of the cemetery was completed by tracking down all the actors who were likely to have information on the bodies, including municipal and national institutions, associations supporting migrants, and key individuals such as the forensic doctors who are called in from time to time by the public prosecutor's office to examine the corpses. The local Red Cross Committee formalised these exchanges in order to provide systematic access to the documents produced by the various offices. A first agreement was signed in March 2018 with the City Council of Catania, so as to obtain the cooperation (and the data) of the civil registry office, the municipal funeral service, the cemetery, and any other institution that might have information related to the dead. Next, an agreement was set up with the judicial authorities, which granted the team access to the courts and to law enforcement agencies. At the same time, links were established with associations and other actors involved in the landings.

Working on the principle that piecing together all the data on a particular body could provide some leads as to its identity, the project's aim became that of constructing a database gathering all the existing information that could potentially help to identify the unknown bodies and, subsequently, to find their families. The database was thus intended as a tool for storing and linking data that had previously been contained in a wide variety of documents: death certificates, forensic inspection forms, survivors' statements obtained before the landing, declarations of a search for a relative, and objects found with the body. 8The collection of information depended entirely on Silvia, Riccardo, and Davide, who regularly visited the offices of the civil registry, the cemetery, the police forensics department, etc., to consult the available documents and talk to the people who had dealt with the files. Once a firstand technically very simpleversion of the database had been built, the small team examined the collated information in order to find elements that could lead to an identification. They had discussions with key partners within the institutions, for example, within the squadra mobile if the leads came from a report, or from the civil registry if it concerned information from their offices. This made it possible to test hypotheses and to obtain more precise details about, for example, the context in which a statement was taken, or the source that provided a first name recorded on a death certificate. These discussions allowed the team to re-examine the information, then consult other institutional actors, revisit leads, and follow up on new ones. Although the small team were at the centre of this delicate work, many employees of the funeral service, the civil registry office, and law enforcement agencies actively participated in the handling of this information.

Working with the official documents concerning the deceased, whether to integrate them into the database or collectively to follow a trail that could lead to an identity, is not without consequences. This is true both for the members of the RFL team and for the state officials involved in the project. These materialities have haunting qualities (see Autcher 2014).

Bringing the dead home

The people approached by the Red Cross team, working in the various institutions concerned with the management of the dead, warmly welcomed the project from the outset. All of them, without exception, stressed the importance of compensating for the lack of any official investigation aimed at identifying these dead. During our stays in Catania, we accompanied the members of RFL to the offices of the civil registry office, the funeral service, the squadra mobile, and the police forensics department. Whatever their biographical background, all our interlocutors were particularly affected by the youth of the dead. We observed the prevalence of an empathetic tone when speaking about these dead who were "Others", usually in opposition to a Catanese, Sicilian, Italian, or European "We/Us". Thus, Mrs Giordano, who was responsible for processing their files at the civil registry office, said to us in March 2018: "Those poor people, when I think about them, I think that they left to find a better life, for themselves, for their families, just as we would do. They're like us, well… like you [she laughed], they were young, they're like our young people". Ms Pessina, from the police forensics department, expressed a similar view during a discussion on social inequalities: "the only difference between these young people and our young people is that they didn't have the same opportunities".

The words of our interlocutors stress the humanity that is shared with these dead, by establishing a clear analogy between, on the one hand, "our" young people or the young people "from here", and on the other hand, "those" young people. These words, imbued with humanistic or even humanitarian emotions, were accompanied by practices that manifest a particular attention towards the deceased which, as we shall see later, go beyond humanitarianism and partake of a new affective political grammar. The act of attending their burial was significant for the people we met. Mrs Giordano recalls in particular the burial of several bodies in 2015. It was the first time she had seen coffins "buried on top of each other". It was a "very cold" and "unpleasant" moment, but she does not regret having participated. On the contrary, "it was important to accompany them". Mr Mancini, Mr Ricci, and Mr Gulino from the funeral service speak in the same terms. They all remember this moment as being unusual because it was devoid of the ceremony that often surrounds burials, being without family, names, or tears. And yet, as they all recall, it was also a moment of great intensity, which they have difficulty putting into words. Other people, who were not present at the burials, are accustomed to paying their respects in front of the black plaques of the "migrants' square" when they go to the cemetery to visit their deceased loved ones. This is the case of some Red Cross volunteers, as well as the former military chaplain who previously belonged to the Corpo nazionale dei Vigili del Fuoco, the fire and rescue service, whom we contacted to ask him about the forms of religious rites that take place on the boats when transporting people who have died at sea. At the end of our conversation, he told us that his parents are buried in an alley near the "migrants' square" and that he places a flower in front of each of the plaques. "Only God knows the names and number of the dead, but they are people and this is a way of honouring them". He often takes a few extra steps to pay his respects at the graves of the monument.

Other practices further introduce these dead into the daily lives of the people involved in the project. As Mr Mancini expressed it, "li portiamo a casa" [we bring them home with us]. He wanted us to understand that the bitter memory of having to deal with these bodies stayed with him and his colleagues outside of working hours. Mr Mancini told us several times how he sometimes talks to his wife about these "poor young people", sharing his pain regarding the youth and loneliness of the dead, but mostly remaining silent about the degradation of the remains. Mrs Pessina also talks about it at home, especially to her teenage daughter. This started when her daughter asked her about the sea rescues and the condition of the bodies. "She's aware of what's happening, she sensitive to it and wants to understand". So her mother found it natural to talk to her about them, and commented that "it's also good that she knows certain things". Mrs Pessina tells her daughter how the landings happen, how she goes about examining the bodies for particular traces that could help identify them, but also the few details she has about who these people were when they were alive, where they came from, how old they were, in order to "get an idea of who they were".

Unlike Mrs Pessina and Mr Mancini, other people involved in the project prefer to avoid talking too much about the dead at home in order to "protect" their children or partners, to spare them from the pain and sorrow that they themselves feel. Riccardo tells us that he does not want to "burden" his wife and children (who are young adults) but that he soon felt the need to talk about it outside the circle of the Red Cross. He began writing long emails to a close friend and started keeping a diary of his experiences during the landings. This allowed him to share his suffering as well as his anger regarding the treatment of the living and the dead. Silvia's experience is fairly similar. She does not reveal much at home about her emotions and activities related to her involvement with RFL, but she discusses them with a few close friends, with whom she talks about the few scraps of life stories of the dead that she has.

Talking about the dead outside the space devoted to their treatment is a way of introducing them into the sphere of friendly and family relations. In these discussions, those who have died in the Mediterranean often appear as a relatively homogeneous group of people who deserve to be respected, honoured, and commemorated. Sometimes, however, conversations revolve around a particular dead person: a man and woman who drowned but whose forensic reports indicated serious illnesses and who were the subject of many hypotheses as to their relationship (a married couple or siblings?), or the case of a young child whose travelling companions were unknown, but who was buried next to a woman. The bodies of these individuals, or the fragments of their stories that appear somewhere on a document, were presumably particularly striking. During discussions, some interlocutors do not hesitate to name these dead by borrowing first names or surnames that appear in the testimony of a fellow traveller or somewhere in a document concerning them, which are not the result of an identification process but which allow them to avoid the use of administrative termssince, in discussions relating to the database, a body is usually referred to by the code given to it in the cemeteryand thus to individualise them. The dead also enter the lives of those involved in the project through their appearance in the latter's dreams. Many employees of the funeral service have nightmares in which those who have died at sea are decomposed, alone, or lost, and in which the person having the dream is unable to care for them. The thought of the bad state of these bodies can also arise unexpectedly in the waking hours. This is what one of the most discreet employees of the funeral service told us, in an aside, who mentioned seeing "the bodies of migrants in tatters" when his mother served him a dish of pasta with tomatoes. For other interlocutors, those who do not come into direct contact with the bodies, it is not so much their condition as the solitude of the dead that often emerges at night while they sleep.

Seeing the dead in dreams, talking about them to one's friends or relatives, and visiting them in the cemetery are all fairly minor acts, which may even seem unimportant. However, they were all attached to the work and activities that each of our interlocutors carried out within the various institutions, and to the narratives they gave us of those activities. Together, these acts, these narratives, and this work show how the dead haunt our interlocutors. They also afford us an insight into some of the afterlives of those who have died in the Mediterranean. Through these practices and discourses, affective ties and relationships of connectedness with the dead are woven, which are at the heart of the emergence of a new social inscription of the dead. This inscription takes place through our interlocutors who, by means of their practices and discourses, "prolong" -to use Vinciane Despret's term (2015, 88) the existence of these dead by giving them a place in their own lives.

A new family inscription

The relationship between, on the one hand, our interlocutors and, on the other hand, the dead and the place given to them, is not clearly defined. It is, at the very least, a form of relatedness. With this term, Janet Carsten (2000) aims to extend the concept of kinship and to emphasise the existence of relationships that can develop in the course of everyday experiences as a process involving emotions. This concept is undoubtedly too broad for our purpose, but it has the merit of stressing the emotionality and connectedness that is established through relatively trivial actions, which corresponds perfectly to our observations in Catania.

In fact, the forms of attachment to the dead that we have observed seem to have features that draw them closer to the realm of kinship, perhaps even in a fairly narrow sense of the term. Anthropologists have explored the relationships that develop between the dead and the living through the prism of kinship. Thus, Heonik [START_REF] Kwon | Ghosts of War in Vietnam[END_REF], in his ethnography on ghosts from the wars in Vietnam, has shown how "ontological refugees", those Vietnamese who died far from home and had no burial place, were adopted in the 1990s by villagers who saw them appear and incorporated them into their families. The researcher relates how, at the request of Lotus Flower, the spirit of a ten-year-old girl who died during the war and manifested itself through the body of a sixteen-year-old girl, the latter's parents decided to adopt the ghost. An adoptive kinship between the deceased and the host family was thus established. Buddhist Laotians can also engage in kinship relationships with the dead. These are ghosts (phiphed) who have lost their humanity owing to ethical failure or a bad death, and who are in Hell. Patrice [START_REF] Ladwig | Visitors from Hell: Transformative Hospitality to Ghosts in a Lao Buddhist Festival[END_REF] examines how through hospitalitythe first gesture of which is that of feeding the ghosts -and the construction of an "artificial" kinship, these dead, who were at first anonymous, can be reintegrated into the world of humans. Unlike these cases in Vietnam or Laos, in Catania the ties of connectedness that are established with those who have died in the Mediterranean are never put into wordsat least, not in the course of our researcheither by the people who take care of them or through the stories that are told about them, as is the case in Laos. None of the interviewees used terms relating to kinship to describe the material and emotional ties that bind them to the dead. However, the attachment and affective engagement that emerge through small, everyday acts, as well as the place that the dead acquire "in the homes" of the Catanese, bear witness to a form of incorporation of the foreign dead among their hosts, through the creation of a "ritualised kinship". This is based, according to Julian [START_REF] Pitt-Rivers | The Kith and Kin[END_REF], on an analogy with the nuclear family, and involves a principle of simulation by which the characteristics associated with "real" kinship are attributed to a tie of connectedness that one wishes to consolidate.9 Giovanni Da Col has more recently used this concept in relation to that of hospitality, a concept that was also explored by [START_REF] Pitt-Rivers | The Law of Hospitality[END_REF][START_REF] Pitt-Rivers | The Law of Hospitality[END_REF]). Hospitality is then conceived as:

[a] system of strategies and ritualised kinship (Pitt-Rivers 1974) for a subject (the host), possessing agency over a territory or a domestic domain, for keeping the stranger in abeyance or incorporating the outside into the inside. The actions involved in hospitality rituals are characteristic of rites of incorporation and are capable of establishing bonds analogous to adoption of new kinship or similar affinal ties. (Da Col 2019, 20) [emphasis in original] Although we have a reservation regarding the strategic dimension of hospitality relationships noted here, which does not seem to us to correspond to the relationships that our interlocutors establish with the dead whom they care for, the definition proposed corresponds fairly well to the observations made in Catania. The affective engagement with the dead and the feelings of connectedness cannot be detached from a concern for hospitality.

From the beginning of the project, Silvia, Riccardo, and Davide emphasised the hospitality dimension of their initiative. Silvia stressed the fact that it was "about hospitality, about giving dignity to the dead", while Riccardo spoke of a "minimal act of hospitality". In their minds, it was above all a matter of "respecting" the dead by offering them the hospitality that they should have had while still alive. In other words, hospitality towards the dead was presented as the antithesis of the hostile treatment that was afforded to living migrants. For Silvia, Riccardo, and Davide this involved both a set of practices aimed at caring for the dead (by making them exist in their own lives and also by reuniting them with their families) and the public condemnation of the inhospitable and murderous character of the contemporary border regime in Europe. In this respect, in Jacques Derrida's sense of the term, hospitality is political as it becomes something else that is the principle or law of "unconditional hospitality" [START_REF] Derrida | De l'hospitalité[END_REF]. It is a form of hospitality as politics, that generates "spaces of appearance and belonging that are, in fact, interrupting the current suspension of the laws of hospitality" (Oberprantacher 2013, 164). This political dimension is probably not shared by all the people involved in the project; for example, no member of the police force mentioned the question of political responsibility for the dead. However, all our interlocutors mentioned the importance of "welcoming" and receiving with dignity these dead from elsewhere.

Whether it is considered as a form of political mobilisation or as an act of humanity, or as a humanitarian action, the hospitality advocated by our interlocutors is eminently public. However, the relationships they have with the dead and the affects that are involved give this hospitality an additional, more intimate dimension. Furthermore, the intimate, private, and public experiences of the ties of hospitality and relationships of connectedness with the dead are constantly intertwined. In his diary, Riccardo relates a scene during a landing that allows us to grasp this intertwining of the public and private. He describes how he told a Red Cross volunteer, who wondered why she could not contain her tears when witnessing a lifeless body being brought ashore from a large ship, carried by employees of the funeral service, "we are, and must remain human, and the dead must be mourned". For Riccardo, mourning this dead man, knowing only that he comes from the other side of the sea, means recognising both the humanity of the deceased and that of those who mourn him. It also means offering a place in the world to one who, when living, was considered undesirable: "it's the least we can do, a minimal act of hospitality". The tears of this volunteer, like those of our interlocutors, shed either in a public space or out of sight, crystallise the emotion felt at the moment of the "encounter" with the deadwhether this is the moment of taking charge of the body or of handling their case through the databaseand the affective tie that is then formed. They also crystallise a kind of mourning that is both intimate and political. Acting, in a sense, in place of the families who, without any news of the death of their loved ones, cannot mourn them, our interlocutors take on a form of mourning by proxy [START_REF] Furri | The Place of the Dead in the Mediterranean: A Sicilian Experience[END_REF]. Through their actions and engagements, they assume the right to mobilise for these dead and the responsibility to keep their memory alive. In a way, they also take on board the logics of haunting and learn "to live with" (Derrida, 1993, 15) the spectres in their daily lives ("in the upkeep, the conversation, the company, or the companionship […] of ghosts", thus engaging in extending open hospitality to them.

Hospitality relationships (both intimate and political), ties of connectedness resembling forms of kinship, and the (private and public) experience of mourning combine to induce a shift in "the distribution of the sensible". With this concept, Jacques [START_REF] Rancière | The Politics of Aesthetics. The Distribution of the Sensible[END_REF] refers to the way in which modes of participation in a common social world are determined by establishing possible modes of perception. In this sense, the distribution of the sensible establishes divisions between what is visible and invisible, "sayable" and "unsayable", audible and inaudible. Our interlocutors in Catania expand the visibility of the dead, making them exist in their own lives. Without completely setting aside the emotions at the heart of humanitarianism, they thus produce a new affective grammar at the border, a grammar that, to quote Miriam Ticktin (2016, 268), "goes beyond the temporality of the emergency at the heart of humanitarianism to include the timelessness of death". This configuration "render[s] it impossible to escape these bodies" and as a result "their images haunt us, acting as witnesses, and demanding justice."

The duration of ties and their transformative potential

As numerous studies have helped to show, death at Europe's borders is a direct effect of tightening security policies and migration control techniques [START_REF] Albahari | Crimes of Peace: Mediterranean Migrations at the World's Deadliest Border[END_REF][START_REF] Weber | Globalization and Borders: Death at the Global Frontier[END_REF]. The power to expose people to death is an expression of European sovereignty that manifests itself daily. It haunts those who attempt the crossing, but as we showed it also acts on those who are tasked with the management of the dead, with whom they are not (in principle) affiliated. In this article we have looked at an initiative in the city of Catania where a group of inhabitants have developed a unique form of hospitality towards those who have died in the Mediterranean, consisting of trying to identify them and return them to their families. We briefly described the setting up of the project and focused on the ways in which this work quickly gave rise to an emotional attachment to the dead. These affective ties are manifested in the treatment of the body (from the moment of its arrival), and in the work surrounding the database, but above all in the private and even intimate sphere of our interlocutors. A new kind of affiliation with the dead arises from these relationships of connectedness, one that is reminiscent of forms of elective kinship that allow newcomers to be included in a collective.

The bodies of border crossers who died in the Mediterranean and were buried in Catania, or elsewhere in Italy, are, for the most part, destined to remain there indefinitely. As Brightman and Grotti (2019, 253) point out, this reality runs counter to one of the fundamental elements of the laws of hospitality, namely, that host-guest relationships are by definition temporary. Hospitality is only a phase, it "foresees its own overcoming" (Agier 2018, 33), whether through social incorporation or else through departure, rejection, or abandonment. The ultimate aim of the database project is that of identifying the bodies and returning them to the families. In this sense, the hospitality that is offered to them has a time limit. This limit is, of course, difficult to measure, but the practices implemented are designed to last only a short time. The forms of attention given to the dead are intended to continue only until the moment when their families take on the role of caring for them.

The families of the dead were at the centre of the process from the beginning, and even before this point, since the driving force behind this initiative came from a Red Cross programme aimed at promoting the family ties that are placed at risk by migration. "Everything we do, we do for the living", said Riccardo in a conversation with Silvia and Davide, before adding, as his friends nodded, "respecting the dead means respecting them as people, it also means respecting their relatives". We can thus consider that the practices deployed with regard to the dead are intended as a substitute for those that, in the view of the people involved in the project, would otherwise be carried out by the family members of the deceased. By further developing the figure of substitution, or that of a fictitious or ritualised kinship, we can think of our interlocutors as substitute parents, brothers, or sisters for these "young people".

Although the project is beginning to show positive results and the first identifications achieved through the database are now official, it is still too early to know what will happen to this new kinship when some of the dead are returnedprobably symbolically rather than materiallyto their homes after being identified. When this hospitality has run its course, the relationship established with the identified dead will be transformed. It then remains to be seen what kind of links may develop with the living associated with the dead (their parents, their "real" children), possibly leading to other ways of keeping their memories alive.

Studying public practices of mourning at the US-Mexico border, Alexandra Délano and Benjamin Nienass (2016, 443) affirm that political transformation through mourning seems often to be reserved for those who were already seeking it by engaging in these activities in the first place. The same could be claimed here. The initiators of the project, already committed to migrants within the Red Cross, are probably those for whom the change is clearest. But as the authors show for the North-American border here too there may be space for transformation and the emergence of counter narratives elsewhere. A number of public employees who have developed very close ties with the dead and engaged in a form of vicarious mourning, no longer see migrants as they used to. Police officers, civil registry employees, and municipal undertakers shared with us their belief that they now have another perception of newcomers. Many of our interlocutors who, according to their own statements, were previously not particularly sensitive to migration issues, now feel this way. "When I see migrants in the street or read about a disembarkation somewhere in Italy or Greece or Spain, I cannot help thinking of these dead people", said one employee of the civil registry office while pointing at the documents on her desk, "I don't see things in the same way anymore". This is a "more fraternal" conception of migrants, "stripped of the media images that distance them from us", as one police inspector told us. These discourses make us think that proximity and connectedness to the unknown dead buried in Catania has led to a variation in the "distribution of the sensible". In other words, this experience has, in a way, refined our interlocutors' perceptions, bringing to the forefront silenced deaths and lives.10 During our fieldwork, we have not (yet) been able to observe whether these discourses have a correlate in our interlocutors' professional practices, but we believe that the close attachment to the dead migrants experienced by the officials involved in the project may lead to some measure of change in how they treat migrants within their professional practices. While this new affective grammar may not entail a radical political change, it is possible that it will lead to a shift in border policies from within public offices.

See https://missingmigrants.iom.int/region/mediterranean[accessed 12 November 2021]. The IOM has been producing statistics on border deaths since 2013. Contrary to the migrant defence collectives that had initiated the project of counting border deaths in order to make the harmful effects of the border regime visible through the publicisation of figures, the IOM disconnects the figures of deaths from the environment in which they occur[START_REF] Heller | Counting Migrants' Deaths at the Border : From Civil Society Counterstatistics to (Inter)Governmental Recuperation[END_REF]. Despite this depoliticisation, the statistics show an exponential increase since the 2000s of lives lost on migratory routes owing to the restrictions placed on movement that push those attempting the crossing to areas where they are exposed to the "facts of nature", thereby transforming the sea and the desert into places of death[START_REF] Schindel | Bare Life at the European Borders: Entanglements of Technology, Society and Nature[END_REF].

It should be noted that the fight against people-smugglers, which is emphasised by governments, tends to obscure the responsibility of the policies implemented by the European Union (see Babels 2017).

This is with the exception of three shipwrecks that received extensive media coverage, for which the national authorities made substantial resources available to work on identifying the victims. The tragedies of 3 October 2013 and 18 April 2015 in the central Mediterranean were the subject of an exceptional protocol[START_REF] Cattaneo | Naufraghi senza volto: Dare un nome alle vittime del Mediterraneo[END_REF], as was the shipwreck in the Otranto Channel on 28 March 1997.

International coalition created in 2011 to defend the rights of migrants at sea.

The names of our interlocutors have been changed to ensure anonymity and confidentiality, except for the members of RFL who initiated the project. These are referred to by their real names, in accordance with their wishes.

For more details on the design of the database and the documents from which the data were collected, see our earlier paper(Furri and Kobelinsky 2019).

AsPitt-Rivers (1974, 98) notes, the bond is initiated only on the basis of mutual agreement, which does not seem to be the case here. It should be noted that Pitt-Rivers is speaking here about ties of friendship that are formalised through an analogy with kinship, such as the relationship of compadrazgo in Andalusia.

The use of sight in this excerpt ("When I see migrants…"; "I don't see things…") is noteworthy, since the visibility of border deathsand more broadly of unauthorized migrantsis a key political issue.

Funding details

This work was supported by the MECMI Research Programme (ANR-16-FRQSC-2-2017-2021, dir. Kobelinsky & Rachédi) and the CORTEM Programme (ANR, dir. N. Fischer).