2. Definitions and Remarks If F is class of objects of a category C, by an F-precover of an
object X of C we mean a morphism: F→ X with FF such that Hom (G, F')→ Hom (G, X) is …

Let A, C be categories, JH a full subcategory of C, X:. M—* C the inclusion functor and T; M—
*—> A a full and faithful functor. Denote by 9^ CI) the category of all full and faithful functors …

Each full reflective subcategory X of a finitely-complete category C gives rise to a
factorization system (E, M) on C, where E consists of the morphisms of C inverted by the …

1. Introduction. In a category (€, an object Q will be said to be injective with respect to a
morphism/: A-> B if for every (¡): A-+ Q there exists\¡/: B^ Q such that</>=\¡/f. An injective …

PURE-INJECTIVE ENVELOPES Page 1 November 5, 2003 12:16 WSPC/171-JAA 00058
Journal of Algebra and Its Applications Vol. 2, No. 4 (2003) 397–402 c© World Scientific …

The notions of reflexive and coreflexive subcategories in topology have received much
attention in the recent past.(See eg Kennison [5], Herrlich [2], Herrlich and Strecker [4] …

We establish equivalent conditions under which every object in an Abelian category has a
monic X-cover and an epic X-envelope respectively, when X is a class of objects closed …

THE COMPLETION OF AN ABELIAN CATEGORY Page 1 TRANSACTIONS OF THE
AMERICAN MATHEMATICAL SOCIETY Volume 170, August 1972 THE COMPLETION OF AN …

Consider, to begin with, decompositions of complete categories as products or as
coproducts. However, a complete category cannot be a coproduct of two or more nonempty …

1. Introduction. In this paper we present some conditions which are sufficient to ensure the
existence of injective envelopes in a category, and we mention some categories where …