Let (C, E, s) be an extriangulated category. We show that certain quotient categories of
extriangulated categories are equivalent to module categories by some restriction of functor …

For a triangulated category TT, if CC is a cluster-tilting subcategory of TT, then the factor
category T/CT/C is an abelian category. Under certain conditions, the converse also holds …

In this article, we study the Gorenstein property of abelian quotient categories induced by
fully rigid subcategories on an exact category B. We also study when d-cluster tilting …

We introduce the notion of pre-weight structure on a triangulated category and study the
corresponding pseudo-identities. We propose the notion of canonical derived equivalence …

Let $\mathcal {C} $ be an extriangulated category and let $\mathcal {R}\subseteq\mathcal
{C} $ be a rigid subcategory. Generalizing Iyama--Yang silting reduction, we devise a …

Gentle and Todorov proved that in an abelian category with enough projective objects, the
extension subcategory of two covariantly finite subcategories is covariantly finite. We give an …

It is a well established fact that the notions of quasi-abelian categories and tilting torsion
pairs are equivalent. This equivalence fits in a wider picture including tilting pairs of $ t …

Many definitions of weak and strict $\infty $-categories have been proposed. In this paper we
present a definition for $\infty $-categories with strict associators, but which is otherwise fully …

In Corollary 4.2 we showed that for subcategories C of mod II closed under extensions of the
form C= Sub M there are only a finite number of nonisomorphic indecomposable objects in …

Given small dg categories A and B and a BA-bimodule T, we give necessary and sufficient
conditions for the associated derived functors of Hom and the tensor product to be fully …