Sheaf theory is a mathematical framework that allows for the systematic study of local data that can be glued together to form global data. This concept is particularly useful in algebraic geometry and topology, where local properties can often be analyzed through their relationships to larger structures. It connects deeply with category equivalence, the Yoneda lemma, topoi, and Kan extensions by providing a way to handle local-global principles and understand how different spaces and categories relate through sheaves.
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