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Mathlib.CategoryTheory.Sites.Localization

The sheaf category as a localized category #

In this file, it is shown that the category of sheaves Sheaf J A is a localization of the category Presheaf J A with respect to the class J.W of morphisms of presheaves which become isomorphisms after applying the sheafification functor.

@[reducible, inline]

The class of morphisms of presheaves which become isomorphisms after sheafification. (See GrothendieckTopology.W_iff.)

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    @[deprecated CategoryTheory.GrothendieckTopology.W_sheafToPresheaf_map_iff_isIso (since := "2025-07-27")]

    Alias of CategoryTheory.GrothendieckTopology.W_sheafToPresheaf_map_iff_isIso.