Model category structures and spectral sequences

Abstract: Model categories give an abstract setting for homotopy theory, allowing study of different notions of equivalence. I'll give a very brief introduction and review some standard examples, such as the projective model structure on chain complexes. Then I'll discuss various categories with associated functorial spectral sequences. In such settings, one can consider a hierarchy of notions of equivalence, given by morphisms inducing an isomorphism at a fixed stage of the associated spectral sequence. I'll discuss model structures with these weak equivalences for filtered complexes, for bicomplexes and for multicomplexes. This involves joint work with subsets of Joana Cirici, Daniela Egas Santander, Xin Fu, Ai Guan and Muriel Livernet.

Mathematics

Audience: researchers in the topic

Opening Workshop (IRP Higher Homotopy Structures 2021, CRM-Bellaterra)