{"id":921,"date":"2018-03-06T15:22:29","date_gmt":"2018-03-06T15:22:29","guid":{"rendered":"http:\/\/www.lmpa.univ-littoral.fr\/SIC\/?page_id=921"},"modified":"2018-03-06T15:22:29","modified_gmt":"2018-03-06T15:22:29","slug":"seminaire-du-18-mai-2018-a-lille","status":"publish","type":"page","link":"https:\/\/www-lmpa.univ-littoral.fr\/~sic\/wordpress\/?page_id=921","title":{"rendered":"S\u00e9minaire du 12 octobre 2018 \u00e0 Lille"},"content":{"rendered":"

ATTENTION : Ce SIC remplace celui initialement annonc\u00e9 pour le 18 mai 2018, report\u00e9 \u00e0 cause de la “gr\u00e8ve perl\u00e9” SNCF du printemps dernier.<\/i><\/span><\/p>\n

Lieu<\/strong> : Universit\u00e9 de Lille, Laboratoire de Math\u00e9matiques, B\u00e2timent M2, Salle de r\u00e9union.<\/p>\n

Organisation<\/strong> :<\/p>\n

Ivo Dell\u2019Ambrogio <ivo.dell-ambrogio@univ-lille.fr>
\nIsar Stubbe <isar.stubbe@lmpa.univ-littoral.fr>
\nAlexis Virelizier <alexis.virelizier@univ-lille.fr><\/p>\n

Ce SIC est soutenu financi\u00e8rement par la F\u00e9d\u00e9ration de Recherche Math\u00e9matique du Nord-Pas-de-Calais et par le Labex CEMPI.<\/p>\n

Participation<\/strong> :<\/p>\n

La participation au SIC est gratuite. Pour des raisons pratiques, on demande aux participants de s\u2019inscrire. Pour cela, un simple mail \u00e0 un des organisateurs suffit. Le repas de midi sera offert aux participants inscrits avant le 1 octobre.<\/span>
\nLors de l’inscription, veuillez nous communiquer votre choix entre les deux plats suivants :
\n1) supr\u00eame de poulet sauce foresti\u00e8re (poultry meat),
\n2) dos colin cr\u00e8me citronn\u00e9 (fish).
\nLe repas comprendra aussi un buffet d’hors d’oeuvres et un buffet de desserts.<\/p>\n

Programme<\/strong> :<\/p>\n

10h15 : Accueil avec caf\u00e9<\/i>
\n10h50 \u2013 11h40 : Jacques Darn\u00e9 (Grenoble)
\n11h50 \u2013 12h40 : Tom Hirschowitz (Chamb\u00e9ry)
\nRepas \u00e0 l\u2019Ascotel<\/i>
\n14h00 \u2013 14h50 : Simon Henry (Brno)
\n15h00 \u2013 15h50 : Paolo Saracco (Bruxelles)
\nPause caf\u00e9<\/i>
\n16h10 \u2013 17h00 : Idriss Tchoffo Nguefeu (Louvain-la-Neuve)<\/p>\n

<\/a> Titres des expos\u00e9s :<\/strong><\/p>\n

Jacques Darn\u00e9 : Actions in the category of N-series<\/i> (r\u00e9sum\u00e9<\/a>).
\nTom Hirschowitz : Foncteurs polynomiaux et carr\u00e9s exacts en s\u00e9mantique des jeux<\/i>.
\nSimon Henry : La conjecture de strictification de Simpson<\/i> (r\u00e9sum\u00e9<\/a>).
\nPaolo Saracco : Tannaka-Kre\u012dn reconstruction and coquasi-bialgebras with preantipode<\/i> (r\u00e9sum\u00e9<\/a>).
\nIdriss Tchoffo Nguefeu : Connecteurs et groupo\u00efdes internes dans les categories de Goursat<\/i> (r\u00e9sum\u00e9<\/a>).<\/p>\n

Participants (ordre d’inscription)<\/strong> :<\/p>\n

Ivo Dell’Ambrogio (Lille)
\nIsar Stubbe (Calais)
\nAlexis Virelizier (Lille)
\nJacques Darn\u00e9 (Grenoble)
\nSimon Henry (Brno)
\nTom Hirschowitz (Chamb\u00e9ry)
\nPaolo Saracco (Bruxelles)
\nIdriss Tchoffo Nguefeu (Louvain-la-Neuve)
\nAndr\u00e9e Ehresmann (Amiens)
\nGiulio Calimici (Lille)
\nIvan Bartulovic (Lille)
\nAntoine Touz\u00e9 (Lille)
\nJames Huglo (Lille)
\nJun Maillard (Lille)
\nDominique Bourn (Calais)
\nJohn Robert (Bruxelles)
\nElisabeth Vaugelade (Amiens)
\nDaniel Tanr\u00e9 (Lille)
\nHuafeng Zhang (Lille)
\nAur\u00e9lien Djament (Lille)
\nBenoit Fresse (Lille)
\nTim van der Linden (Louvain-la-Neuve)
\nAmine Laaroussi (Lille)
\nHongyi Chu (Lille)<\/p>\n

Informations utiles<\/strong> :<\/b><\/p>\n

Pour venir \u00e0 Lille :
\nGoogle maps<\/a>
\nPlan d’acc\u00e8s<\/a>
\nInstructions d\u00e9taill\u00e9es<\/a><\/p>\n

Pour dormir \u00e0 Lille :
\nOffice de Tourisme de Lille<\/a><\/p>\n

R\u00e9sum\u00e9s :<\/strong>
\n<\/a><\/p>\n

<\/a> Jacques Darn\u00e9 :<\/strong> Actions in the category of N-series<\/i><\/p>\n

N-series are nicely-behaved filtrations on groups, linked to their nilpotent structure. We will introduce a category of N-series. This category is homological, and the general definition of actions in such categories apply. It admits universal actions, which are linked to generalized Johnson morphisms. We will describe how this language allows us to get an interesting point of view on some classical constructions, and to get some new results about them. (Retour \u21a9<\/a>)<\/p>\n

<\/a> Simon Henry :<\/strong> La conjecture de strictification de Simpson<\/i><\/p>\n

In ’91, Kapranov and Voevodsky erroneously claimed to prove that every weak infinity groupoid (homotopy type) is equivalent to one in which all the composition operations (except inverses) are strict, i.e. a strict infinity category with weak inverse. This is now known to be false, but Carlos Simpson conjectured in ’98 that any weak infinity groupoid is equivalent to one were all composition operations are strict, except units and inverses, i.e. a “non-unital strict infinity category” with weak units and weak inverses. He also mentioned that Kapranov and Voevodsky’s paper might contains the proof of this claim. In this talk I will present very recent progress on this conjecture, including a first proof of a form of the conjecture in arbitrary dimension, and which indeed use the same ideas as Kapranov and Voevodsky’s original proof. (Retour \u21a9<\/a>)<\/p>\n

<\/a> Paolo Saracco :<\/strong> Tannaka-Kre\u012dn reconstruction and coquasi-bialgebras with preantipode<\/i><\/p>\n

Via the Tannaka-Kre\u012dn formalism it is possible to construct a Hopf algebra from a rigid monoidal category endowed with a monoidal “fiber” functor to finitely-generated and projective k<\/i>-modules. In particular, this allows us to characterize Hopf algebras over a field as those bialgebras whose category of finite-dimensional corepresentations is rigid. In this talk, we report on an analogue reconstruction theorem and we show how a rigid monoidal category with a quasi<\/i>-monoidal “fiber” functor gives rise to a coquasi-bialgebra with preantipode (as introduced by Ardizzoni and Pavarin). When k<\/i> is a field, this allows us to characterize coquasi-bialgebras with preantipode and coquasi-Hopf algebras in terms of the rigidity of their categories of finite-dimensional comodules.<\/p>\n

As an application, we will endow the finite dual coalgebra of a quasi-bialgebra with preantipode with the structure of a coquasi-bialgebra with preantipode. (Retour \u21a9<\/a>)<\/p>\n

<\/a> Idriss Tchoffo Nguefeu :<\/strong> Connectors and internal categories in Goursat categories<\/i><\/p>\n

(Joint work with Marino Gran and Diana Rodelo.) Given two equivalence relations $(R, r_1, r_2)$ and $(S, s_1, s_2)$ on the same object $X$, we denote by $R\\times_X S$ the pullback
\n\\[\\begin{matrix}
\nR\\times_X S & \\rightarrow & S \\\\
\n\\downarrow & & \\downarrow s_1 \\\\
\nR & \\stackrel{r_2}{\\rightarrow} & X
\n\\end{matrix}\\]
\nIn a finitely complete category $\\mathcal{C}$ a connector [2] between $R$ and $S$ is an arrow $p\\colon R\\times_X S \\rightarrow X$ such that (internally)
\n$\\bullet xSp(x,y,z)Rz$;
\n$\\bullet p(x,x,y) = y$ and $p(x,y,y) = x$,
\n$\\bullet p(x,y,p(z,u,v))=p(p(x,y,z),u,v)$,
\nwhenever each term is defined. One of the main interests of the notion of connector is that it allows one to study centrality of equivalence relations in any Mal’tsev category even without defining the commutator of equivalence relations. Also in any Goursat category [1] a connector between $R$ and $S$ is unique when it exists, since the Shifting Lemma holds in any Goursat category [3]. In this talk, we prove that connectors are stable under quotients in any regular Goursat category. As a consequence, the category $Conn(\\mathcal{C})$ of connectors in $\\mathcal{C}$ is a Goursat category whenever $\\mathcal{C}$ is. This implies that Goursat categories can be characterised in terms of a simple property of internal groupoids [4]. We finally prove that regular Mal’tsev and Goursat categories can be characterised through stronger variations of the Shifting Lemma [5].
\nReferences
\n[1] A. Carboni, G.M. Kelly, M.C. Pedicchio, Some remarks on Mal’tsev and Goursat categories, Appl. Categ. Structures 1 (1993), no. 4, 385-421.
\n[2] D. Bourn and M. Gran, Centrality and connectors in Maltsev categories, Algebra Universalis 48 (2002), no. 3, 309-331.
\n[3] D. Bourn and M. Gran, Categorical Aspects of Modularity, Galois Theory, Hopf Algebras and Semiabelian Categories, Fields Instit. Commun. 43, A.M.S., Providence RI (2004) 77-100.
\n[4] M. Gran, D. Rodelo, I. Tchoffo Nguefeu, Some remarks on connectors and groupoids in Goursat categories, Logical Methods in Computer Science (2017), vol.13(3:14), 1-12.
\n[5] M. Gran, D. Rodelo, I. Tchoffo Nguefeu, Variations of the Shifting Lemma and Goursat categories, preprint, http:\/\/arxiv.org\/abs\/1809.10408 (2018). (Retour \u21a9<\/a>)<\/p>\n","protected":false},"excerpt":{"rendered":"

ATTENTION : Ce SIC remplace celui initialement annonc\u00e9 pour le 18 mai 2018, report\u00e9 \u00e0 cause de la “gr\u00e8ve perl\u00e9” SNCF du printemps dernier. Lieu : Universit\u00e9 de Lille, Laboratoire de Math\u00e9matiques, B\u00e2timent M2, Salle de r\u00e9union. Organisation : Ivo Dell\u2019Ambrogio <ivo.dell-ambrogio@univ-lille.fr> Isar Stubbe <isar.stubbe@lmpa.univ-littoral.fr> Alexis Virelizier <alexis.virelizier@univ-lille.fr> Ce SIC est soutenu financi\u00e8rement par la […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":96,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"_links":{"self":[{"href":"https:\/\/www-lmpa.univ-littoral.fr\/~sic\/wordpress\/index.php?rest_route=\/wp\/v2\/pages\/921"}],"collection":[{"href":"https:\/\/www-lmpa.univ-littoral.fr\/~sic\/wordpress\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www-lmpa.univ-littoral.fr\/~sic\/wordpress\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www-lmpa.univ-littoral.fr\/~sic\/wordpress\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www-lmpa.univ-littoral.fr\/~sic\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=921"}],"version-history":[{"count":0,"href":"https:\/\/www-lmpa.univ-littoral.fr\/~sic\/wordpress\/index.php?rest_route=\/wp\/v2\/pages\/921\/revisions"}],"up":[{"embeddable":true,"href":"https:\/\/www-lmpa.univ-littoral.fr\/~sic\/wordpress\/index.php?rest_route=\/wp\/v2\/pages\/96"}],"wp:attachment":[{"href":"https:\/\/www-lmpa.univ-littoral.fr\/~sic\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=921"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}