Extriangulated categories were introduced by Nakaoka and Palu as a simultaneous
generalization of exact categories and triangulated categories. In this paper, we introduce …

We show that a right triangulated category is best behaved when its shift satisfies conditions
making it what we call a right semi-equivalence. We consider right triangulated categories …

For a compactly generated triangulated category we gives a new proof for the fact that the
category of modules over its subcategory consisting of all compact objects it is not only the …

In representation theory, the double centralizer property is an important property for a
module (bimodule). In this paper, we extend this property to complexes in derived categories …

The author proves that a recollement of triangulated categories can induce a recollement of
quotient categories naturally. In particular, the second isomorphism theorem of triangulated …

We study the category $\operatorname {Rep}(Q,\mathcal {C}) $ of representations of a
quiver $ Q $ with values in an abelian category $\mathcal {C} $. For this purpose we …

Tannaka duality is concerned with the reconstruction of a coalgebra in the category of vector
spaces from its category of finite dimensional representations equipped with its forgetful …

We explore some similarities between the theory of D-modules and that of quasi-coherent
sheaves of categories. The original motivation is to better understand several results on the …

This paper focuses on a question raised by Holm and J {\o} rgensen, who asked if the
induced cotorsion pairs $(\Phi ({\sf X}),\Phi ({\sf X})^{\perp}) $ and $(^{\perp}\Psi ({\sf Y}),\Psi …

We investigate the behavior of the extension dimension of subcategories of abelian
categories under recollements. Let Λ′, Λ, Λ ″be artin algebras such that (mod Λ′, mod Λ …