In this paper,(dual) purely Rickart objects are introduced as generalizations of (dual) Rickart
objects in Grothendieck categories. Examples showing the relations between (dual) relative …

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 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 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 …

Crossed Semimodules of Categories and Schreier 2-Categories Page 1 Crossed Semimodules
of Categories and Schreier 2-Categories Sedat Temel Department of Mathematics, Recep …

In this paper we study generalizations of the concept of pure-direct-injectivity from module
categories to Grothendieck categories. We examine for which categories or under what …

Atomical Grothendieck categories Page 1 IJMMS 2003:71, 4501–4509 PII. S0161171203209418
http://ijmms.hindawi.com © Hindawi Publishing Corp. ATOMICAL GROTHENDIECK …

We introduce and study (strongly) π-Rickart objects and their duals in abelian categories,
which generalize (strongly) self-Rickart objects and their duals. We establish general …