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 …

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 …

Let $\mathcal C $ be a Krull-Schmidt triangulated category with shift functor $[1] $ and
$\mathcal R $ be a rigid subcategory of $\mathcal C $. We are concerned with the mutation …

Let $\mathcal {A} $ be a Hom-finite abelian category with enough projectives. In this note,
we show that any covariantly finite $\tau $-rigid subcategory is contained in a support $\tau …

Let be an extriangulated category with enough projectives P \mathcalP and enough
injectives I \mathcalI, and let be a contravariantly finite rigid subcategory of which contains P …

Let CC be a triangulated category with shift functor 1 and RR a contravariantly rigid
subcategory of C C. We show that a tilting subcategory of mod\, R mod R lifts to a two-term …

We introduce the higher version of Adachi-Iyama-Reiten's support τ-tilting pairs, which are
regarded as a generalization of maximal τ n-rigid pairs in the sense of Jacobsen-Jørgensen …