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 …

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

Full article: Pure-direct-objects in categories: transfer via functors Skip to Main Content Taylor and
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The classical Cantor-Bernstein-Schröder Theorem states that if A and B are two sets such
that there exist injective functions f: A→ B and g: B→ A, then there exists a bijection between …

The general theory of Grothendieck categories is presented. The Popescu-Gabriel
generalized theorem and theorems for projective generating families are proved. Due to …

We generalize to exact categories some new perspectives on projectivity, which allow us to
unify a series of recent concepts from module categories or abelian categories and to obtain …

On projectivity in locally presentable categories Page 1 Journal of Algebra 272 (2004) 701–710
www.elsevier.com/locate/jalgebra On projectivity in locally presentable categories J …

Given any additive category C with split idempotents, pseudokernels and pseudocokernels,
we show that a subcategory B is coreflective if, and only if, it is precovering, closed under …

It is well known that over a left Notherian ring any direct sum of injecive modules is again
injective, and every injective module is a direct sum of indecomposable modules. Faith [6] …

In this paper we discuss some of the major functorial properties of module categories over
topoi, and in particular their closed structure. The primary theorem is a general version of …