Abstract In [16], a theory of universal extensions in abelian categories is developed; in
particular, the notion of Ext 1-universal object is presented. In the present paper, we show …

There are well-known identities involving the Ext bifunctor, coproducts, and products in AB4
abelian categories with enough projectives. Namely, for every such category\[\mathcal {A}\] …

In an arbitrary Grothendieck category, we find necessary and sufficient conditions for the
class of FP n-injective objects to be a torsion class. By doing so, we propose a notion of n …

EXT-GROUPS, DOLD k-INVARIANT AND FORMALITY Contents Introduction 1
Acknowledgments 2 1. Postnikov tower and k-invariant 2 1.1. P Page 1 EXT-GROUPS, DOLD …

In the context of semi-abelian categories, we develop some new xaspects of the categorical
theory of central extensions by Janelidze and Kelly. If C is a semi-abelian category and X is …

In this article, we develop the obstruction theory for lifting complexes, up to quasi-
isomorphism, to derived categories of flat nilpotent deformations of abelian categories. As a …

We consider an arbitrary Abelian category A and a subcategory T closed under extensions
and direct summands, and characterize those T that are (semi-) special preenveloping in A; …

3. RESULTS We start by answering negatively the question of Colby and Fuller referred to
above, in the simpler case of abelian categories. EXAMPLE 1. Let~ 2 be the full subcategory …

Our study starts with investigating the fundamental relations between the subcategories
defined above. Then we concentrate on the subcategories P, X and S, respectively. As …

We study an exactness condition that allows us to treat many of the familiar constructions in
abelian categories and toposes in parallel. Examples of such constructions include …