Axiomatic Sheaf Cohomology Theories

Abstract

The aim of this thesis is to define and use the notion of a sheaf to define cohomology theories. These sheaf cohomology theories will be defined in an axiomatic way and then showed to be unique. Then a few of such cohomology theories will be defined, such as Cech, de Rham and Singular and these theories will be related to classical definitions of cohomology.