Introduction. The natural setting for a theory of sheaves is a site, iea category C topologized
in the sense of Grothendieck(cf. VERDIER[1963]). We shall consider a sheaf A of rings on a …

In this paper we prove that any sheaf of modules over any topological space (in fact, any
$\mathcal {O} $-module where $\mathcal {O} $ is a sheaf of rings on the topological space) …

Sheaves on topological spaces were invented by Jean Leray as a tool to deduce global
properties from local ones. Then Grothendieck realized that the usual notion of a topological …

Let ${\mathbf {A}} $ be the category of sheaves of universal algebras of some fixed type on a
Grothendieck topology. There is defined a cohomology theory ${H^\ast} $ such that if $ A $ is …

Two new definitions are given for cup products in the cohomology of sheaves on an arbitrary
Grothendieck topology. These products are shown to have the usual properties. The …

We study the cohomology theory of sheaf complexes for open embeddings of topological
spaces and related subjects. The theory is situated in the intersection of the general Čech …

This book is primarily concerned with the study of cohomology theories of general
topological spaces with" general coefficient systems." Sheaves play several roles in this …

For a site S (with enough points), we construct a topological space X (S) and a full
embedding ϕ∗ of the category of sheaves on S into those on X (S)(ie, a morphism of …

The word “homology” comes from the classical Greek words ὁμός (meaning “same”) and
λόγος (meaning “discourse” among other things), so it might be rendered as “discourse …

In this essay we develop the basic idea of a sheaf, look at some simple examples and
explore areas of mathematics which become more transparent and easier to think about in …