English
Homotopy theory of strict $\omega$-categories and its connections with homology of monoids - Lecture 1
Post-edited
Auteurs : Métayer, François (Auteur de la Conférence)
CIRM (Editeur )
18D05 - Double categories, $2$-categories, bicategories, hypercategories
18G10 - Resolutions; derived functors
18G50 - Nonabelian homological algebra
18G55 - Homotopical algebra
CIRM (Editeur )
Loading the player...
|
| lifting properties model structures Smith's theorem $\omega$-categories weak equivalences cylinder category |
Résumé :
In the first part, we describe the canonical model structure on the category of strict $\omega$-categories and how it transfers to related subcategories. We then characterize the cofibrant objects as $\omega$-categories freely generated by polygraphs and introduce the key notion of polygraphic resolution. Finally, by considering a monoid as a particular $\omega$-category, this polygraphic point of view will lead us to an alternative definition of monoid homology, which happens to coincide with the usual one.
Codes MSC : 18D05 - Double categories, $2$-categories, bicategories, hypercategories
18G10 - Resolutions; derived functors
18G50 - Nonabelian homological algebra
18G55 - Homotopical algebra
|
Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 28/09/2017 Date de captation : 25/09/2017 Sous collection : Research talks arXiv category : Category Theory ; Algebraic Topology Domaine : Logic and Foundations ; Algebra ; Topology Format : MP4 (.mp4) - HD Durée : 01:27:34 Audience : Researchers Download : https://videos.cirm-math.fr/2017-09-25_Metayer_Part1.mp4 
|
Informations sur la Rencontre
Nom de la rencontre : Categories in homotopy theory and rewriting / Catégories pour la théorie de l'homotopie et la réécritureOrganisateurs de la rencontre : Ara, Dimitri ; Fiore, Marcelo ; Guiraud, Yves ; Mimram, Samuel Dates : 25/09/2017 - 29/09/2017 Année de la rencontre : 2017 URL Congrès : http://conferences.cirm-math.fr/1773.html
Données de citation
DOI : 10.24350/CIRM.V.19225303Citer cette vidéo: Métayer, François (2017). Homotopy theory of strict $\omega$-categories and its connections with homology of monoids - Lecture 1. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19225303 URI : http://dx.doi.org/10.24350/CIRM.V.19225303 |
Voir aussi
- [Multi angle] Type theories and polynomial monads / Auteur de la Conférence Awodey, Steve.
- [Multi angle] Shuffles of trees / Auteur de la Conférence Hoffbeck, Eric.
- [Multi angle] Homotopy theory of strict $\omega$-categories and its connections with homology of monoids - Lecture 3 / Auteur de la Conférence Métayer, François.
- [Multi angle] Homotopy theory of strict $\omega$-categories and its connections with homology of monoids - Lecture 2 / Auteur de la Conférence Métayer, François.
Bibliographie
- Beke, T. (2000). Sheafifiable homotopy model categories. Mathematical Proceedings of the Cambridge Philosophical Society, 129(3), 447-475 - http://dx.doi.org/10.1017/s0305004100004722
- Burroni, A. (1993). Higher-dimensional word problems with applications to equational logic. Theoretical Computer Science, 115(1), 43-62 - http://dx.doi.org/10.1016/0304-3975(93)90054-w
- Hovey, M. (1999). Model Categories. Providence, RI: American Mathematical Society - https://zbmath.org/?q=an:0909.55001
- Lafont, Y., & Metayer, F. (2009). Polygraphic resolutions and homology of monoids. Journal of Pure and Applied Algebra, 213(6), 947-968 - http://dx.doi.org/10.1016/j.jpaa.2008.10.005
- Lafont, Y., Metayer, F., & Worytkiewicz, K. A folk model structure on omega-cat. Advances in Mathematics, 224(3), 1183-1231 - http://dx.doi.org/10.1016/j.aim.2010.01.007
- Metayer, F. (2008). Cofibrant objects among higher-dimensional categories. Homology, Homotopy and Applications, 10(1), 181-203 - http://dx.doi.org/10.4310/hha.2008.v10.n1.a7
- Street, R. (1987). The algebra of oriented simplexes. Journal of Pure and Applied Algebra, 49(3), 283-335 - http://dx.doi.org/10.1016/0022-4049(87)90137-x
