Covers and Directed Colimits Page 1 Algebr Represent Theor (2006) 9: 423–430 DOI
10.1007/s10468-006-9030-5 Covers and Directed Colimits Robert El Bashir Received: 1 …

In the general setting of Grothendieck categories with enough projectives, we prove
theorems that make possible to restrict the study of the problem of the existence of F-covers …

We prove general results about completeness of cotorsion theories and existence of covers
and envelopes in locally presentable abelian categories, extending the well-established …

We study C-covers in the context of Grothendieck categories. Namely, we analyse when a
functor between two Grothendieck categories preserves or reflects C-covers. We apply our …

The concepts of covers and envelopes of modules have been studied under different guises
by several authors (in the school of Auslander they are called minimal left and right …

We show that if a class of modules is closed under pure quotients, then it is precovering if
and only if it is covering, and this happens if and only if it is closed under direct sums. This is …

Injective covers of modules were introduced by Enochs [5] as a categorical dual of an
injective envelope and they have been investigated by many authors. The T-torsionfree …

The regular and exact completions of categories withweak limits are proved to exist and to
be determined by an appropriate universal property. Several examples are discussed, and …

A morphism f: M→ N of left R-modules is a phantom morphism if for any morphism g: A→ M,
with A finitely presented, the composition fg factors through a projective module …

arXiv:math/9909030v1 [math.CT] 5 Sep 1999 Page 1 arXiv:math/9909030v1 [math.CT] 5 Sep
1999 GROTHENDIECK CATEGORIES GRIGORY GARKUSHA Contents 0. Introduction 1 1 …