We prove that some subquotient categories of exact categories are abelian. This
generalizes a result by Koenig–Zhu in the case of (algebraic) triangulated categories. As a …

In this paper, we consider a kind of ideal quotient of an extriangulated category such that the
ideal is the kernel of a functor from this extriangulated category to an abelian category. We …

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 …

In this paper, we prove that if a triangulated category D admits a recollement relative to
triangulated categories D'and D'', then the abelian category D/T admits a recollement …

Extriangulated categories were introduced by Nakaoka and Palu by extracting the
similarities between exact categories and triangulated categories. A notion of mutation of …

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 …

We investigate how to characterize subcategories of abelian categories in terms of intrinsic
axioms. In particular, we find axioms which characterize generating cogenerating functorially …

Extriangulated category was introduced by H. Nakaoka and Y. Palu to give a unification of
properties in exact categories and triangulated categories. A notion of tilting (resp., cotilting) …

Abstract Let E=(A, S) be an exact category with enough projectives P. We introduce the
notion of support τ-tilting subcategories of E. It is compatible with the existing definitions of …

In this article, we prove that if (A, B, C) is a recollement of extriangulated categories, then
torsion pairs in A and C can induce torsion pairs in B, and the converse holds under natural …