A triangulated category T whose suspension functor Σ satisfies Σ m≅ Id T as additive
functors is called an m-periodic triangulated category. Such a category does not have a …

Let $\mathcal B $ be an extriangulated category with enough projectives and enough
injectives. We define a proper $ m $-term subcategory $\mathcal G $ on $\mathcal B …

In this paper we develop the theory of topological categories over a base category, that is, a
theory of topological functors. Our notion of topological functor is similar to (but not the same) …

The notion of a pseudo cluster tilting subcategory $\mathcal X $ in an extriangulated
category $\mathcal C $ is defined in this article. We prove that the quotient category …

Let C be an extriangulated category and τ be any n-cluster tilting subcategory of C. We
consider the index with respect to τ and introduce the index Grothendieck group of τ. Using …

Assume that $\mathcal {D} $ is a Krull-Schmidt, Hom-finite triangulated category with a Serre
functor and a cluster-tilting object $ T $. We introduce the notion of relative cluster tilting …

Motivated by the concept of a torsion pair in a pre-triangulated category induced by
Beligiannis and Reiten, the notion of a left (right) torsion pair in the left (right) triangulated …

In the previous article “Hearts of twin cotorsion pairs on exact categories. J. Algebra, 394,
245–284 (2013)”, we introduced the notion of the heart for any cotorsion pair on an exact …

Abstract Suppose\((\mathcal {C},\mathbb {E},\mathfrak {s})\) is an n-exangulated category.
We show that the idempotent completion and the weak idempotent completion of\(\mathcal …

Extriangulated categories were introduced by Nakaoka and Palu to give a unification of
properties in exact categories and extension-closed subcategories of triangulated …