On the monomorphism category of n-cluster tilting subcategories

Abstract

Let ℳ be an n-cluster tilting subcategory of mod-Λ, where Λ is 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−ℳ¯, 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−ℳ¯. We also compare these two functors and show that they differ by the n-th syzygy functor, provided ℳ is an nℤ-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] / 〈 xn〉 and generalized later by Eiríksson (2017) to self-injective Artin algebras. Several applications are provided. © 2021, Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature.