On the Monomorphism Category of n-Cluster Tilting Subcategories [article]

Javad Asadollahi, Rasool Hafezi, Somayeh Sadeghi
2020 arXiv   pre-print
Let M be an n-cluster tilting subcategory of modΛ, where Λ is an artin algebra. Let S(M) denotes the full subcategory of S(Λ), the submodule category of Λ, consisting of all monomorphisms in M. We construct two functors from S(M) to modM, the category of finitely presented (coherent) additive contravariant functors on the stable category of M. We show that these functors are full, dense and objective. So they induce equivalences from the quotient categories of the submodule category of M modulo
more » ... their respective kernels. Moreover, they are related by a syzygy functor on the stable category of modM. These functors can be considered as a higher version of the two functors studied by Ringel and Zhang [RZ] in the case Λ=k[x]/〈 x^n 〉 and generalized later by Eiríksson [E] to self-injective artin algebras. Several applications will be provided.
arXiv:2008.04178v1 fatcat:w3igeaczbjasbhmvy24fkakmkm