Theorems · Definition · category theory

CategoryTheory.Presheaf.sheafificationIsoImagePresheaf

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    (J : CategoryTheory.GrothendieckTopology C) →
      (F : CategoryTheory.Functor Cᵒᵖ (Type (max u v))) →
        J.sheafify F ≅
          (CategoryTheory.Subfunctor.sheafify J (CategoryTheory.Subfunctor.range (J.toSheafify F))).toFunctor

The image of F in J.sheafify F is isomorphic to the sheafification.

Defined in: Mathlib.CategoryTheory.Sites.LocallySurjective
Cited by: 0 results in Mathlib
Foundations: Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category

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CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Functorstatement and proof · cited by 16,252
Oppositestatement and proof · cited by 8,081
CategoryTheory.Isostatement · cited by 3,963
CategoryTheory.GrothendieckTopologystatement and proof · cited by 1,415
CategoryTheory.GrothendieckTopology.Coverstatement · cited by 211
CategoryTheory.Limits.WalkingMulticospanstatement · cited by 199
CategoryTheory.Limits.MulticospanIndex.multicospanstatement · cited by 167
CategoryTheory.GrothendieckTopology.Cover.shapestatement · cited by 147
CategoryTheory.GrothendieckTopology.Cover.indexstatement · cited by 142
CategoryTheory.Subfunctor.toFunctorstatement · cited by 90
CategoryTheory.Subfunctor.ιproof · cited by 50

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