Injective Objects of Monomorphism Categories
Keyan Song, Zhanping Wang, Yuehui Zhang

TL;DR
This paper characterizes injective objects in monomorphism categories over acyclic quivers and finite-dimensional algebras, showing their structure, existence of enough injectives, and applications to tilting theory and singularity categories.
Contribution
It provides a unified description of indecomposable injectives in monomorphism categories and establishes their enough-injective property, with applications to tilting and singularity categories.
Findings
Explicit description of indecomposable injectives in ${ m Mon}(Q,A)$
Proof that ${ m Mon}(Q, A)$ has enough injectives
Realization of the singularity category as a stable monomorphism category
Abstract
For an acyclic quiver and a finite-dimensional algebra , we give a unified form of the indecomposable injective objects in the monomorphism category and prove that has enough injective objects. As applications, we show that for a given self-injective algebra , a tilting object in the stable category -mod induces a natural tilting object in the stable monomorphism category . We also realize the singularity category of the algebra as the stable monomorphism category of the module category of .
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Nonlinear Waves and Solitons
