We give a simultaneous generalization of exact categories and triangulated categories,
which is suitable for considering cotorsion pairs, and which we call extriangulated …

Extriangulated categories axiomatize extension-closed subcategories of triangulated
categories and generalise both exact categories and triangulated categories. This survey …

Cluster categories were introduced in 2006 by Buan-Marsh-Reineke-Reiten-Todorov in
order to categorify acyclic cluster algebras without coefficients. Their construction was …

We give a simple sufficient condition for a Verdier quotient ${\cal T}/\{\cal S} $ of a
triangulated category ${\cal T} $ by a thick subcategory ${\cal S} $ to be realized inside of …

We develop the basic properties of $ w $-simple-minded systems in $(-w) $-Calabi-Yau
triangulated categories for $ w\geqslant 1$. We show that the theory of simple-minded …

Let $ Q $ be an acyclic quiver and $ w\geqslant 1$ be an integer. Let $\mathsf {C} _ {-
w}({\mathbf {k}} Q) $ be the $(-w) $-cluster category of ${\mathbf {k}} Q $. We show that there …

Gillespie's Theorem gives a systematic way to construct model category structures on C (M),
the category of chain complexes over an abelian category M. We can view C (M) as the …

In the present paper, we study the relationships of $ n $-cotorsion pairs among three abelian
categories in a recollement. Under certain conditions, we present an explicit construction of …

Abstract Silting and Calabi–Yau reductions are important processes in representation theory
to construct new triangulated categories from given ones, which are similar to Verdier …

The aim of this paper is to provide an expansion of Abe–Nakaoka's heart construction to the
following two different realizations of the module category over the endomorphism ring of a …