This report contains two parts. First, we explore the separated monic correspondence which is extensively used to describe the structure of Gorenstein-projective modules. In this talk, we will show that the correspondence also can be established between (complete) hereditary cotorsion pair in A-mod and that in A ⊗kQ/I-mod for a ffnite acyclic bounded quiver (Q, I). Secondly, we foucs on Auslander - Reitein translation. For an artin algebra Λ, Ringel and Schmidmeier showed a formula for the AR-translation in the submodule module category S(Λ) : τS (f) = Mimo ◦ τΛ ◦ Coker(f), for each f ∈ S(Λ) . With the help of recent works by Hafezi and Eshraghi, we are able to provide a new proof of this formula, which not only provides more insights into the connections between morphism categories and functor categories, but also enjoys broader generaltities. That is, the formula also works for monomorphism categories of certain exact categories. This talk is based on the joint work with Shijie Zhu.