Hideto Asashiba (Shizuoka University / MPI Bonn)

Grothendieck constructions of (co)lax functors and gluing of derived equivalences, I and II.

Abstract:

Let k be a field. We explain a gluing process of derived equivalences of k-categories using Grothendieck constructions of colax functors from a small category I to the 2-category of k-categories. If we have time, we remark on a generalization of this process by extending the definition of Grothendieck constructions to those of lax functors from I to the bicategory of k-categories and bimodules over them to construct derived equivalences between triangular matrix algebras (or more generally tensor algebras of k-species).