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

We introduce the notion of an exact dg category, which is a simultaneous generalization of
the notions of exact category in the sense of Quillen and of pretriangulated dg category in …

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 …

Additive categories play a fundamental role in mathematics and related disciplines. Given
an additive category equipped with a biadditive functor, one can construct its category of …

Palu defined the index with respect to a cluster tilting object in a suitable triangulated
category, in order to better understand the Caldero–Chapoton map that exhibits the …

We extend results of Br\" ustle-Yang on ideal quotients of 2-term subcategories of perfect
derived categories of non-positive dg algebras to a relative setting. We find a new …

We describe a reduction technique for stably 2-Calabi--Yau Frobenius extriangulated
categories $\mathcal {F} $ with respect to a functorially finite rigid subcategory $\mathcal {X} …

We provide new equivalent conditions for an algebra $\Lambda $ to be $ g $-finite,
analogous to those established by L. Demonet, O. Iyama, and G. Jasso, but within the …

Let $\mathcal {C} $ be an extriangulated category and let $\mathcal {R}\subseteq\mathcal
{C} $ be a rigid subcategory. Generalizing Iyama--Yang silting reduction, we devise a …

Quillen's Resolution Theorem in algebraic $ K $-theory provides a powerful computational
tool for calculating $ K $-groups of exact categories. At the level of $ K_0 $, this result goes …