We demonstrate equivalence between two definitions of lower finite highest weight
categories. We also show that, in the presence of a duality, a lower finite highest weight …

arXiv:math/0409598v2 [math.CT] 18 Mar 2005 Vers une axiomatisation de la théorie des
catégories supérieures Page 1 arXiv:math/0409598v2 [math.CT] 18 Mar 2005 Vers une …

We investigate how the concepts of intersection and sums of subobjects carry to exact
categories. We obtain a new characterisation of quasi-abelian categories in terms of …

We introduce subclasses of exact categories in terms of admissible intersections or
admissible sums or both at the same time. These categories are recently studied by Br\" …

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 …

Basing ourselves on Janelidze and Kelly's general notion of central extension, we study
universal central extensions in the context of semi-abelian categories. We consider a new …

We develop axiomatics of highest weight categories and quasi-hereditary algebras in order
to incorporate two semi-infinite situations which are in Ringel duality with each other; the …

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 …

The notion of a subtractive category, recently introduced by the author, is a``categorical
version''of the notion of a (pointed) subtractive variety of universal algebras, due to A. Ursini …

In this paper, we study length categories using iterated extensions. We fix a field k, and for
any family S of orthogonal k-rational points in an Abelian k-category AA, we consider the …