On the monomorphism category of n-cluster tilting subcategories

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