Monomorphism Operator and Perpendicular Operator |
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Authors: | Keyan Song Fan Kong |
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Affiliation: | Department of Mathematics , Shanghai Jiao Tong University , Shanghai , China |
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Abstract: | For a quiver Q, a k-algebra A, and an additive full subcategory 𝒳 of A-mod, the monomorphism category Mon(Q, 𝒳) is introduced. The main result says that if T is an A-module such that there is an exact sequence 0 → T m → … → T 0 → D(A A ) → 0 with each T i ∈ add(T), then Mon(Q, ⊥ T) =⊥(kQ ? k T); and if T is cotilting, then kQ ? k T is a unique cotilting Λ-module, up to multiplicities of indecomposable direct summands, such that Mon(Q, ⊥ T) =⊥(kQ ? k T). As applications, the category of the Gorenstein-projective (kQ ? k A)-modules is characterized as Mon(Q, 𝒢𝒫(A)) if A is Gorenstein; the contravariantly finiteness of Mon(Q, 𝒳) can be described; and a sufficient and necessary condition for Mon(Q, A) being of finite type is given. |
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Keywords: | Contravariantly finite Cotilting modules Derived category Finite type Monomorphism category |
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