In this paper we introduce the notion of pre-simple-minded collection (pre-SMC) of type
$\mathbb {A} $ in the bounded derived categories $\mathcal {D}^{b}(${\rm {\textbf {T}}} $ _p) …

A triangulated category $\mathcal {C} $ with a canonical Bott's isomorphism $[2]\xrightarrow
{\sim} id $ is called a cyclic category in this paper. We give a new notion of stability …

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 …

In this work we introduce the notion of higher $\mathbb {E} $-extension groups for an
extriangulated category $\mathcal {C} $ and study the quotients $\mathcal {X} _ {n+ …

We construct a left adjoint $\mathcal {H}^\text {st}\colon\mathbf {Ex} _ {\infty}\rightarrow\
mathbf {St} _ {\infty} $ to the inclusion $\mathbf {St} _ {\infty}\hookrightarrow\mathbf {Ex} …

Stratifying systems, which have been defined for module, triangulated and exact categories
previously, were developed to produce examples of standardly stratified algebras. A …

Let $\mathcal {G} $ be a fusion category acting on a triangulated category $\mathcal {D} $, in
the sense that $\mathcal {D} $ is a $\mathcal {G} $-module category. Our motivation example …

Discrete derived categories were studied initially by Vossieck ['The algebras with discrete
derived category', J. Algebra 243 (2001) 168–176] and later by Bobiński, Geiß and …

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 …

Let $\mathscr {C} $ be an $ n $-exangulated category. In this note, we show that if $\mathscr
{C} $ is locally finite, then $\mathscr {C} $ has Auslander-Reiten $ n $-exangles. This unifies …