Presheaves and Sheaves (Idea & Basic Definitions)

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We briefly explain the idea behind (pre)sheaves and give the definitions.
We are mainly following "Algebraic Geometry I: Schemes" by Goertz and Wedhorn and Vakil's notes on Algebraic Geometry
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Oh this is a nice introduction. A lot of people dive in by defining presheaves as abelian groups on open sets. But the motivation here makes a lot more sense before jumping into the definitions. Especially tying into the zariski topology.

InfiniteQuest