Work

Quotients of exact categories by pseudo-cluster-tilting subcategories

Year: 2023

Type: article

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

Source: Communications in Algebra

DOI: 10.1080/00927872.2023.2223306

Authors: Jie Xu, Yuefei Zheng

Institution: Northwest A&F University

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Fundamental Research Funds for the Central Universities

Awards: G4466689429, G948849846