Injective Objects of Monomorphism Categories

Abstract

For an acyclic quiver $Q$ and a finite-dimensional algebra $A$, we give a unified form of the indecomposable injective objects in the monomorphism category $\mathrm{Mon}(Q,A)$ and prove that $\mathrm{Mon}(Q,A)$ has enough injective objects. As applications, we show that for a given self-injective algebra $A$, a tilting object in the stable category $\underline{A}$-mod induces a natural tilting object in the stable monomorphism category $\underline{\mathrm{Mon}}(Q,A)$. We also realize the singularity category of the algebra $kQ{\otimes }_{k}A$ as the stable monomorphism category of the module category of $A$.

References in corpus (2)

• The Auslander-Reiten Translation in Submodule Categories
• Monomorphism operator and perpendicular operator