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A CATEGORICAL INTRODUCTION TO SHEAVES

A CATEGORICAL INTRODUCTION TO SHEAVESDAPING is a very useful notion when defining and computing many differentcohomology theories over topological spaces. There are several ways to build up sheaftheory with different axioms; however, some of the axioms are a little bit hard to this paper, we are going to present a natural approach from a CATEGORICAL viewpoint,with some remarks of applications of sheaf theory at the end. Some familiarity with basiccategory notions is assumed for the Motivation12. Definitions and Sheaf43. Direct Limit and Sheafification in Sheafification as an Adjoint Functor124. Exact Sequence155. Induced Direct Inverse Adjunction206. A Brief INTRODUCTION to Sheaf Cohomology21 Conclusion and many occasions, we may be interested in algebraic structures defined over local neigh-borhoods.

A CATEGORICAL INTRODUCTION TO SHEAVES DAPING WENG Abstract. Sheaf is a very useful notion when de ning and computing many di erent cohomology theories over topological spaces.

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