Let CC be a 2-Calabi–Yau triangulated category with two cluster tilting subcategories TT
and U U. A result from Jørgensen and Yakimov (Sel Math (NS) 26: 71–90, 2020) and …

The heart of a cotorsion pair, which is a generalization of the heart of a t-structure, has been
proven to be abelian on triangulated, exact, and extriangulated categories. On the other …

Nakaoka and Palu introduced the notion of extriangulated categories by extracting the
similarities between exact categories and triangulated categories. In this paper, we study …

EXACT SUBCATEGORIES OF TRIANGULATED CATEGORIES Introduction The heart of a t-structure
on a triangulated category C is a full ab Page 1 EXACT SUBCATEGORIES OF …

We prove that an object U in a triangulated category with coproducts is silting if and only if it
is a (weak) generator of the category, the orthogonal class U⊥> 0 contains U, and U⊥> 0 is …

Abstract Herschend-Liu-Nakaoka introduced the notion of n-exangulated categories. It is not
only a higher dimensional analogue of extriangulated categories defined by Nakaoka-Palu …

Let C be an extriangulated category with a proper class ξ of E-triangles. We introduce the
notions of left Frobenius pairs, left (n-) cotorsion pairs and left (weak) Auslander-Buchweitz …

A triangulated category $\mathcal {T} $ whose suspension functor $\Sigma $ satisfies
$\Sigma^ m\simeq\mathrm {Id} _ {\mathcal {T}} $ as additive functors is called an $ m …

In a triangulated category T with a pair of triangulated subcategories X and Y, one may
consider the subcategory of extensions X⁎ Y. We give conditions for X⁎ Y to be triangulated …

In this article, we initiate the study of hereditary extriangulated categories. Many important
categories arising in representation theory in connection with various theories of mutation …