This note compares τ-tilting modules and maximal rigid objects in the context of 2-Calabi-
Yau triangulated categories. Let 𝓒 be a 2-Calabi-Yau triangulated category with suspension …

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

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 …

For ad‐Calabi–Yau triangulated category 𝒷 with ad‐cluster tilting subcategory 𝒯, the
decomposition of 𝒷 is determined by the decomposition of 𝒯 satisfying 'vanishing …

In this paper, the authors introduce a new definition of∞-tilting (resp. cotilting) subcategories
with infinite projective dimensions (resp. injective dimensions) in an extriangulated category …

Abstract If (A, B) and (A′, B′) are co-t-structures of a triangulated category, then (A′, B′)
is called intermediate if A⊆ A′⊆ Σ A. Our main results show that intermediate co-t …

We study abelian quotient categories A= T/J, where T is a triangulated category and J is an
ideal of T. Under the assumption that the quotient functor is cohomological we show that it is …

We give a reduction theorem for silting intervals in extriangulated categories, which we call"
silting interval reduction".%{In triangulated categories, it generalizes Pauksztello …

Cluster categories were defined in [BMRRT] in order to use categorical methods to give a
conceptual model for the combinatorics of cluster algebras, as defined by Fomin and …

In our previous article, we constructed an abelian category from any torsion pair on a
triangulated category. This generalizes the heart of a t-structure and the ideal quotient by a …