2023/03/12 by Jie Xu, Xu, Jie, Yuefei Zheng +1
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2303.06646
openalex publication_date 2023/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.