Tuesday, February 14, 16:30, 7.527
Jan Stovicek (Prague), t-structures in the context of Grothendieck derivators

Abstract:
The motivating question for the talk is what conditions exactly a t-structure on a triangulated category must satisfy for its heart to be a Grothendieck (or at least AB5 abelian) category. Triangulated categories occurring in the nature usually come together with an enrichment - a Frobenius exact category, a Quillen closed model category, an infinity-category, or a Grothendieck derivator. The latter is relatively close in spirit to representation theory of quivers and allows one to fix certain deficiencies of the concept of triangulated category. Here we aim at showing how t-structures interact with this enrichment and at providing a rather general answer to the motivating question. This is a joint project with Manuel Saorin and Simone Virili.