Homotopical algebra may be thought of as the study of homotopy categories in the following
sense. We consider a category C that is equipped with a set (1) of morphisms that we want …

Gentle and Todorov proved that in an abelian category with enough projective objects, the
extension subcategory of two covariantly finite subcategories is covariantly finite. We prove a …

This paper proves Brown Representability for stable categories. These categories are
obtained from additive categories by declaring all morphisms which factor through objects …

Let 𝒞 be a triangulated category. When ω is a functorially finite subcategory of 𝒞, Jøtrgensen
showed that the stable category 𝒞/ω is a pretriangulated category. A pair (𝒳, 𝒴) of …

A notion of mutation pairs of subcategories in an abelian category is defined in this article.
For an extension closed subcategory 𝒵 and a rigid subcategory 𝒟⊂ 𝒵, the subfactor …

Chapter 0 gives a gentle background to the thesis. It begins with some general notions and
concepts from homological algebra. For example, not only are the notions of universal …

A note on abelian quotient categories - ScienceDirect Skip to main contentSkip to article
Elsevier logo Journals & Books Search RegisterSign in View PDF Download full issue Search …

It is well-known that one of the most basic discrete invariants of an abelian, resp.
triangulated, category is its Grothendieck group. This useful characteristic is defined as the …

Let AA be an abelian category with enough projective objects, and let XX be a quasi-
resolving subcategory of A A. In this paper, we investigate the affinity of the Spanier …

For an exact category $\mathcal {E} $ with enough projectives and with a $ d\mathbb {Z} $-
cluster tilting subcategory, we show that the singularity category of $\mathcal {E} $ admits a …