On the monomorphism category of n-cluster tilting subcategories  

作　　者：Javad Asadollahi Rasool Hafezi Somayeh Sadeghi 

机构地区：[1]Department of Pure Mathematics,Faculty of Mathematics and Statistics,University of Isfahan,Isfahan 81746-73441,Iran [2]School of Mathematics and Statistics,Nanjing University of Information Science&Technology,Nanjing 210044,China

出　　处：《Science China Mathematics》2022年第7期1343-1362,共20页中国科学：数学（英文版）

基　　金：supported by a grant from University of Isfahan。

摘　　要：Let M be an n-cluster tilting subcategory of mod-Λ,whereΛis an Artin algebra.Let S(M)denote the full subcategory of S(Λ),the submodule category of Λ,consisting of all the monomorphisms in M.We construct two functors from S(M)to mod-Λ,the category of finitely presented additive contravariant functors on the stable category of M.We show that these functors are full,dense and objective and hence provide equivalences between the quotient categories of S(M)and mod-Λ.We also compare these two functors and show that they differ by the n-th syzygy functor,provided M is an n Z-cluster tilting subcategory.These functors can be considered as higher versions of the two functors studied by Ringel and Zhang(2014)in the case Λ=k[x]/and generalized later by Eiríksson(2017)to self-injective Artin algebras.Several applications are provided.

关 键 词：submodule categories n-abelian categories n-cluster tilting subcategories 

分 类 号：O154.1[理学—数学]