ON SHEAF THEORY AND COHOMOLOGY

Abstract

Sheaf theory provides a language for the discussion of geometric objects of many different kinds. The general purpose of sheaf theory is to obtain global information from local one, or else to define "obstruction" which -characterizes the fact that a local property does not hold globally any more: For example, a continuous map at a point is not always continuous. Hence, sheaf theory is a wide generalization of a part of algebraic topology (e.g. Singular Homology theory, [8]) which corresponds to constant sheaves or, more generally, to locally constant sheaves, [13), (9], [17], [18]. Sheaves play a fundamental role in study of cohomology theories

of general topological spaces. For example, they provide a suitable notation of "global coefficient systems". Moreover, they furnish us with a common method of defining various cohomology theories of comparison between them, [13], [2].