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pro vyhledávání: '"Guetta, Léonard"'
Autor:
Guetta, Léonard, Moser, Lyne
Building on work by Fiore-Pronk-Paoli, we construct four model structures on the category of double categories, each modeling one of the following: simplicial spaces, Segal spaces, $(\infty,1)$-categories, and $\infty$-groupoids. Additionally, we pro
Externí odkaz:
http://arxiv.org/abs/2412.15715
Autor:
Guetta, Léonard, Maltsiniotis, Georges
Publikováno v:
Adv. Math. 448 (2024)
In this article, we introduce a notion of polygraphic homology of a strict $\omega$-category with coefficients in a local system, generalizing the polygraphic homology with coefficients in $\mathbb Z$, introduced by Fran\c{c}ois M\'etayer. We show th
Externí odkaz:
http://arxiv.org/abs/2309.10466
We develop new techniques for constructing model structures from a given class of cofibrations, together with a class of fibrant objects and a choice of weak equivalences between them. As a special case, we obtain a more flexible version of the class
Externí odkaz:
http://arxiv.org/abs/2301.07801
Autor:
Guetta, Léonard
We prove that for any weak test category A, the category of presheaves of groupoids over A models homotopy types in a canonical way. The approach taken is a generalization of Grothendieck's theory of test categories.
Comment: 36 pages
Comment: 36 pages
Externí odkaz:
http://arxiv.org/abs/2209.13346
Autor:
Guetta, Léonard, Maltsiniotis, Georges
Publikováno v:
In Advances in Mathematics June 2024 448
Autor:
Guetta, Léonard
In this dissertation, we compare the "classical" homology of an $\omega$-category (defined as the homology of its Street nerve) with its polygraphic homology. More precisely, we prove that both homologies generally do not coincide and call homologica
Externí odkaz:
http://arxiv.org/abs/2104.12662
Autor:
Guetta, Léonard
Publikováno v:
Journal of Pure and Applied Algebra, Elsevier, 2021, 225 (10)
In this paper, we extend a result of Lafont and M{\'e}tayer and prove that the polygraphic homology of a small category, defined in terms of polygraphic resolutions in the category $\omega$Cat of strict $\omega$-categories, is naturally isomorphic to
Externí odkaz:
http://arxiv.org/abs/2003.10734
Autor:
Guetta, Léonard
Publikováno v:
Higher Structures, 2020, 4(2)
We define a class of morphisms between strict $\omega$-categories called discrete Conduch{\'e} $\omega$-functors that generalize discrete Conduch{\'e} functors between 1-categories and we study their properties related to polygraphs. The main result
Externí odkaz:
http://arxiv.org/abs/1812.05332
Autor:
Guetta, Léonard
Publikováno v:
Topologie générale [math.GN]. Université de Paris, 2021. Français. ⟨NNT : 2021UNIP7010⟩
In this dissertation, we compare the ``classical'' homology of an ω-category (defined as the homology of its Street nerve) with its polygraphic homology. More precisely, we prove that both homologies generally do not coincide and call homologically
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::ea8cc1dddcbe90d12a8f9c3b3729a4bc
https://tel.archives-ouvertes.fr/tel-03469580
https://tel.archives-ouvertes.fr/tel-03469580