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Homotopy theory of strict $\omega$-categories and its connections with homology of monoids - Lecture 1
Post-edited
Authors : Métayer, François (Author of the conference)
CIRM (Publisher )
18D05 - Double categories, $2$-categories, bicategories, hypercategories
18G10 - Resolutions; derived functors
18G50 - Nonabelian homological algebra
18G55 - Homotopical algebra
CIRM (Publisher )
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| lifting properties model structures Smith's theorem $\omega$-categories weak equivalences cylinder category |
Abstract :
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.
MSC Codes : 18D05 - Double categories, $2$-categories, bicategories, hypercategories
18G10 - Resolutions; derived functors
18G50 - Nonabelian homological algebra
18G55 - Homotopical algebra
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 28/09/2017 Conference Date : 25/09/2017 Subseries : Research talks arXiv category : Category Theory ; Algebraic Topology Mathematical Area(s) : Logic and Foundations ; Algebra ; Topology Format : MP4 (.mp4) - HD Video Time : 01:27:34 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2017-09-25_Metayer_Part1.mp4 
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Information on the Event
Event Title : Categories in homotopy theory and rewriting / Catégories pour la théorie de l'homotopie et la réécritureEvent Organizers : Ara, Dimitri ; Fiore, Marcelo ; Guiraud, Yves ; Mimram, Samuel Dates : 25/09/2017 - 29/09/2017 Event Year : 2017 Event URL : http://conferences.cirm-math.fr/1773.html
Citation Data
DOI : 10.24350/CIRM.V.19225303Cite 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 |
See Also
- [Multi angle] Type theories and polynomial monads / Author of the conference Awodey, Steve.
- [Multi angle] Shuffles of trees / Author of the conference Hoffbeck, Eric.
- [Multi angle] Homotopy theory of strict $\omega$-categories and its connections with homology of monoids - Lecture 3 / Author of the conference Métayer, François.
- [Multi angle] Homotopy theory of strict $\omega$-categories and its connections with homology of monoids - Lecture 2 / Author of the conference Métayer, François.
Bibliography
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