A category with finite products and finite coproducts is said to be distributive if the canonical
map A× B+ A× C→ A×(B+ C) is invertible for all objects A, B, and C. Given a distributive …

Given a full subcategory [Fscr] of a category [Ascr], the existence of left [Fscr]-approximations
(or [Fscr]-preenvelopes) completing diagrams in a unique way is equivalent to the fact that …

Introduction. The study of homologically finite subcategories has turned out to be important
in several contexts, especially in the representation theory of artin algebras. In this paper we …

The main results of this paper concern decompositions of an injective module, either as a
direct sum of submodules or as the injective envelope of a direct sum of injective …

In this paper we investigate some properties of dense1 and relative adjoint functors which
we will use extensively in [I]. However it seems that some of these properties are of interest …

Let Rbe a ring with identity. Chase [5] has characterized the right coherent rings; he has
shown that arbitrary products of RR are flat if and only if finitely generated submodules of …

For any module M over an associative ring R, let σ [M] denote the smallest Grothendieck
subcategory of Mod-R containing M. If σ [M] is locally finitely presented the notions of purity …

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For accessible set-valued functors it is well known that weak preservation of limits is
equivalent to representability, and weak preservation of connected limits to familial …

Hom (D,−)−→ Hom (C,−)−→ F−→ 0 such that C and D are compact objects in S (an object X
in S is compact if the representable functor Hom (X,−) preserves arbitrary coproducts). The …