The homotopy relation in a category with weak equivalences

SZYLD, MARTÍN

Paris

Seminario; Catégories supérieures, polygraphes et homotopie seminar; 2018

Institut de Recherche en Informatique Fondamentale (IRIF), CNRS-Universite Paris Diderot

I will present the results of the article (arXiv:1804.04244) which deals with the classical construction of the homotopy category of a model category (which is done by performing a quotient of the arrows by the homotopy relation) in the context of categories with weak equivalences. By studying this situation in an abstract context, one can define a relation of homotopy ?only with respect to the weak equivalences? which yields the desired localization and coincides with the classical one for model categories. As it is usually the case, the proofs of these results, which consider only a family of arrows instead of three, become simpler. In particular, they allowed a generalization to bicategories in a current work with E. Descotte and E. Dubuc, which I will present too if time permits.