Building on work of Jasso, we prove that any projectively generated $ d $-abelian category
is equivalent to a $ d $-cluster tilting subcategory of an abelian category with enough …

Let A be an abelian category and B be the Happel-Reiten-Smalø tilt of A with respect to a
torsion pair. We give necessary and sufficient conditions for the existence of a derived …

Presilting and silting subcategories in extriangulated categories were introduced by Adachi
and Tsukamoto recently, which are generalizations of those concepts in triangulated …

This book provides a unified approach to much of the theories of equivalence and duality
between categories of modules that has transpired over the last 45 years. In particular …

Given an exact category C, we denote by C l the smallest additive subcategory containing
injectives and indecomposable objects which appear as the first term of an almost split …

Let X be a semibrick in an extriangulated category C. Let T be the filtration subcategory
generated by X. We give a one-to-one correspondence between simple semibricks and …

Let $\Lambda $ be a finite dimensional algebra. Let $\mathcal C $ be a functorially finite
exact subcategory of $\Lambda $-mod with enough projective and injective objects and …

In this paper, we show that two constructions form stacks: Firstly, as one varies the $\infty $-
topos, $\mathcal {X} $, Lurie's homotopy theory of higher categories internal to $\mathcal {X} …

Firstly we provide a technique to move torsion pairs in abelian categories via adjoint functors
and in particular through Giraud subcategories. We apply this point in order to develop a …

We define stratified exact categories, which are a class of exact categories abstracting very
general features of the category of modules with a Verma flag in a highest weight category …