The Sheafification Theorem states that for any presheaf, there exists a unique sheaf associated with it, which captures its local properties while maintaining the original global data. This process effectively 'corrects' a presheaf into a sheaf, ensuring that it satisfies the sheaf axioms, like locality and gluing. The theorem highlights how one can derive sheaves from presheaves and emphasizes the importance of local information in defining sheaf properties.
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