Let T be a suitable triangulated category and C a full subcategory of T closed under summands and extensions. An indecomposable object c in C is called Ext-projective if Ext1(c,C)=0. Such an object cannot appear as the endterm of an Auslander-Reiten triangle in C. However, if there exists a minimal right almost split morphism b→c in C, then the triangle x→b→c→ extending it is a so called left-weak Auslander-Reiten triangle in C. We show how in some cases removing the indecomposable c from the subcategory C and replacing it with the indecomposable x gives a new extension closed subcategory C‘ of T and see how this operation is related to Iyama-Yoshino mutation of C with respect to a rigid subcategory. Time permitting, we will see the application of the result to cluster categories of type A.
This video is part of the New Directions in Group Theory and Triangulated Categories seminar series.
