For a Frobenius abelian category $\mathcal {A} $, we show that the category ${\rm
Mon}(\mathcal {A}) $ of monomorphisms in $\mathcal {A} $ is a Frobenius exact category; …

In this paper, is an artin algebra over a commutative artinian ring R, the radical of is denoted
by r, and mod is the category of finitely wx generated left-modules. The definitions, notation …

Ž. We recall that a ring R with identity is said to be of finite representation type if it is right
artinian and has only finitely many isomorphism Ž. Ž classes of finitely generated …

An additive category with direct limits is said to be locally finitely presented provided that the
full subcategory of finitely presented objects is skeletally small and every object is a direct …

Extriangulated categories were introduced by Nakaoka and Palu as a simultaneous
generalization of exact categories and triangulated categories. A notion of proper class in an …

Let $ T_R $ be a right $ n $-tilting module over an arbitrary associative ring $ R $. In this
paper we prove that there exists an $ n $-tilting module $ T'_R $ equivalent to $ T_R $ which …

The monomorphism category S n (X) is introduced, where X is a full subcategory of the
module category A-mod of an Artin algebra A. The key result is a reciprocity of the …

Let A be a self-injective artin algebra and X a finitely generated module. In this paper, we are
mainly concerned with the problem posed by Tachikawa [16]: If Ext"(X, X)= 0 for all n> _ 1, is …

Let $\Lambda $ be an artin algebra, let $\bmod\Lambda $ be the category of finitely
generated $\Lambda-{\text {modules}} $, and let $ p {d_1}\bmod\Lambda $ be the …

Let Λ be an elementary locally bounded linear category over a field with radical squared
zero. We shall show that the bounded derived category D b (Mod b Λ) of finitely supported …