Categorification of cluster algebras has instilled the idea of mutation in representation theory. Nice theories of mutation, for some forms of rigid objects, have thus been developed in various settings. In a collaboration with Mikhail Gorsky and Hiroyuki Nakaoka, we axiomatized the similarities between most of those settings under the name of 0-Auslander extriangulated categories. The prototypical example of a 0-Auslander extriangulated category is the category of two-term complexes of projectives over a finite-dimensional algebra. In this talk, we will give several examples of 0-Auslander categories, and explain how they relate to two-term complexes.
This is based on joint work with Xin Fang, Mikhail Gorsky, Pierre-Guy Plamondon, and Matthew Pressland and is related to works by Xiaofa Chen and by Dong Yang.
This video is part of the New Directions in Group Theory and Triangulated Categories seminar series.
