The usual statements of the classical adjoint-functor theorems contain the hypothesis that
the codomain category should admit arbitrary intersections of families of monomorphisms …

This works originates from an attempt to take advantage of the formal analogy between the
cohomology theory with of a space with coefficients in a sheaf [4, 5] and the theory of derived …

Let (F-,. F) be a hereditary torsion theory in a category Mod-R of unital right R-modules over
a ring R with identity 1 and 3'a reflective subcategory of Mod-R such that the left adjoint of …

Classical algebraic geometry begins with the category Algk/, red of finitely generated,
reduced algebras over an algebraically closed field k. The opposite category is the category …

The author has shown in a recent paper [4] that one may dehne a semisimplicial homotopy
theory in any arbitrary category admitting a suitable" cone-functor"(more precisely, a non …

This problem was investigated by M. Husek (see [11]) who introduced a construction
producing a solution F which is the greatest one. His cons-truction works for functors V of the …

If W is a small category (the class of all its morphisms is a set) and if T. is a category, we may
consider the category (I, 9N): the objects are all covariant functors from W to 9C, the …

It is shown that, for a semi-topological functor T: A→ X, the category A is total, that is, the
Yoneda embedding of A has a left adjoint, if X is total. In particular, monadic categories over …

0.1. In this paper we introduce the notion of the basic ring of a] ocally artinian Grothendieck
category cg. Namely let W be the minimal injective cogenerator of~ g, 9] the subcategory of …

The notations for derived categories and derived functors are those of HARTSHORNE [3].
Capital letters X, Y, z, design locally compact Haussdorff spaces1 A is a ring with unity given …