Sheaves: Hartshorne I.1

This lecture covers the concept of sheaves, starting with the definition and properties according to Hartshorne I.1. It explains the notion of a pre-sheaf of abelian groups on a topological space, detailing the construction and properties of sheaves. The lecture delves into the definition of a sheaf as a contravariant functor from the category of open sets to the category of abelian groups, emphasizing the importance of local data. It also explores the distinction between presheaves and sheaves, highlighting the unique determination of functions by local data. The lecture concludes with a discussion on direct limits and their application in defining sheaves.