François Métayer: Homotopy theory of strict omega-categories and its connections with...Part 1

Abstract: In the first part, we describe the canonical model structure on the category of strict ω-categories and how it transfers to related subcategories. We then characterize the cofibrant objects as ω-categories freely generated by polygraphs and introduce the key notion of polygraphic resolution. Finally, by considering a monoid as a particular ω-category, this polygraphic point of view will lead us to an alternative definition of monoid homology, which happens to coincide with the usual one.

Recording during the thematic meeting "Categories in Homotopy Theory and Rewriting" the September 25, 2017 at the Centre International de Rencontres Mathématiques (Marseille, France)

Filmmaker: Guillaume Hennenfent

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