![[1241] Théorie de l’homotopie motivique et groupes d’homotopie stables, d’après Morel–Voevodsky, Isaksen–Wang–Xu, ...](/media/cache/video_light/uploads/video/Bourbaki.png)
publiée le 19 juin 2025
[1241] Théorie de l’homotopie motivique et groupes d’homotopie stables, d’après Morel–Voevodsky, Isaksen–Wang–Xu, ...
De Frédéric Déglise
Homotopy theory of strict $\omega$-categories and its connections with homology of monoids - Lecture 1
Apparaît dans la collection : Categories in homotopy theory and rewriting / Catégories pour la théorie de l'homotopie et la réécriture
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.
