2022/02/14 by Ramin Ebrahimi, Ebrahimi, Ramin, Alireza Nasr‐Isfahani +1
Mathematics · #16E30 #18E99 #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.2202.06711
openalex publication_date 2022/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we introduce nℤ-abelian and nℤ-exact categories by axiomatising properties of nℤ-cluster tilting subcategories. We study this categories and show that every nℤ-cluster tilting subcategory of an abelian (resp., exact) category has a natural structure of an nℤ-abelian (resp., nℤ-exact) category. Also we show that every small nℤ-abelian category arise in this way, and discuss the problem for nℤ-exact categories.