We introduce and study relative Rickart objects and dual relative Rickart objects in abelian
categories. We show how our theory may be employed in order to study relative regular …

We introduce and investigate weak relative Rickart objects and dual weak relative Rickart
objects in abelian categories. Several types of abelian categories are characterized in terms …

We introduce and study (dual) strongly relative Rickart objects in abelian categories. We
prove general properties, we analyze the behaviour with respect to (co) products, and we …

We show how the theory of (dual) strongly relative Rickart objects may be employed in order
to study strongly relative regular objects and (dual) strongly relative Baer objects in abelian …

We study the transfer of (dual) relative Rickart properties via functors between abelian
categories, and we deduce the transfer of (dual) relative Baer property. We also give …

We introduce relative CS-Rickart objects in abelian categories, as common generalizations
of relative Rickart objects and extending objects. We study direct summands and (co) …

We define the notions of Azumaya category and Brauer group in category theory enriched
over some very general base category V. We prove the equivalence of various definitions, in …

Based on the concept of double central extension from categorical Galois theory, we study a
notion of commutator which is defined relative to a Birkhoff subcategory B of a semi-abelian …

To any additive category, we associate in a functorial way two additive categories A (), B ().
The category A (), resp. B (), is the reflection of in the category of additive categories with …

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 …