Quotients of exact categories by pseudo-cluster-tilting subcategories

Abstract

We introduce the concept of a pseudo-cluster-tilting subcategory from the viewpoint of the fact that the quotient of an exact category by a cluster-tilting subcategory is an abelian category. We prove that the quotients in the case of pseudo-cluster-tilting are always semi-abelian. In addition, it is abelian if and only if some self-orthogonal conditions are satisfied. We revisit the abelian quotient category of conflations by splitting ones, and get that there exists a unique exact substructure such that it is a cluster quotient. Communicated by Julia Plavnik