H 2 Homotopy theory of strict $\omega$-categories and its connections with homology of monoids - Lecture 1

Auteurs : Métayer, François (Auteur de la Conférence)
CIRM (Editeur )

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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

    Langue : 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 : Chercheurs ; Doctorants , Post - Doctorants
    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 réécriture
Organisateurs 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

Citation Data

DOI : 10.24350/CIRM.V.19225303
Cite this video as: 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

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