Let $ R $ be a commutative ring If $\mathcal {C} _1 $ and $\mathcal {C} _2 $ are $ R $-linear
triangulated categories then we can give an obvious triangulated structure on $\mathcal …

In the theory of triangulated categories, we propose to replace hearts of $ t $-structures by
proper abelian subcategories, which may be plentiful even when hearts are not. For …

We prove that certain subquotient categories of extriangulated categories are abelian. As a
particular case, if an extriangulated category CC has a cluster-tilting subcategory XX, then …

In this work we introduce notions in Auslander-Buchweitz theory and cotorsion theory in
extriangulated categories which extend the given ones for abelian categories. Although …

We consider the ordinary category Span (C) of (isomorphism classes of) spans of
morphisms in a category C with finite limits as needed, composed horizontally via pullback …

arXiv:1206.6632v2 [math.CT] 7 May 2015 Page 1 A COURSE ON DERIVED CATEGORIES
AMNON YEKUTIELI Contents 0. Introduction 2 0.1. A motivating discussion: duality 3 1. Basics …

arXiv:2308.10815v1 [math.CT] 21 Aug 2023 Page 1 UNIVERSAL SUPPORT FOR
TRIANGULATED CATEGORIES PAUL BALMER AND PABLO S. OCAL Abstract. We revisit a …

Let $\mathscr {A} $ be an extension closed proper abelian subcategory of a triangulated
category $\mathscr {T} $, with no negative 1 and 2 extensions. From this, two functors from …

A non-self-contained gathering of notes on category theory, including the definition of locally
cartesian closed category, of the cartesian structure in slice categories, or of the pseudo …