Quotients of exact categories by pseudo-cluster tilting subcategories
Representation Theory
2023-03-14 v1 Category Theory
K-Theory and Homology
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.
Keywords
Cite
@article{arxiv.2303.06646,
title = {Quotients of exact categories by pseudo-cluster tilting subcategories},
author = {Jie Xu and Yuefei Zheng},
journal= {arXiv preprint arXiv:2303.06646},
year = {2023}
}