2013/01/14 by Keyan Song, Pu Zhang, Song, Keyan +1
Mathematics · #16E65 #16G10 #16G50 #16G60 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1301.2853
openalex publication_date 2013/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a quiver Q, a k-algebra A, and a full subcategory \mathcal X of A-mod, the monomorphism category \rm Mon(Q, \mathcal X) is introduced. The main result says that if T is an A-module such that there is an exact sequence 0→ Tm→...→ T0→ D(AA)→ 0 with each Ti∈ \rm add (T), then \rm Mon(Q, ^⊥ T) = ^⊥ (kQ⊗k T); and if T is cotilting, then kQ⊗k T is a unique cotilting \m-module, up to multiplicities of indecomposable direct summands, such that \rm Mon(Q, ^⊥ T)= ^⊥ (kQ ⊗k T). As applications, the category of the Gorenstein-projective (kQ⊗kA)-modules is characterized as \rm Mon(Q, GP(A)) if A is Gorenstein; the contravariantly finiteness of \rm Mon(Q, \mathcal X) can be described; and a sufficient and necessary condition for \rm Mon(Q, A) being of finite type is given.