Theorems · Theorem · category theory
CategoryTheory.classifier_isSheaf
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (J₁ : CategoryTheory.GrothendieckTopology C),
CategoryTheory.Presieve.IsSheaf J₁ (CategoryTheory.Functor.closedSieves J₁).toFunctorThe presheaf of J-closed sieves is a J-sheaf.
The proof of this is adapted from [MM92], Chapter III, Section 7, Lemma 1.
- Defined in
- Mathlib.CategoryTheory.Sites.Closed
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites45
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homproof · cited by 32,603
- CategoryTheory.Functor.objproof · cited by 19,642
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- Top.topproof · cited by 9,680
- CategoryTheory.Functor.mapproof · cited by 8,698
- Oppositestatement · cited by 8,081
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- le_antisymmproof · cited by 2,068
- Quiver.Hom.opproof · cited by 1,948
- le_rflproof · cited by 1,558
Cited by4
Results whose statement or proof uses this declaration.
- CategoryTheory.CoverPreserving.of_isContinuousproof · cited by 2
- CategoryTheory.GrothendieckTopology.mem_iff_isSheafFor_closedSievesproof · cited by 2
- CategoryTheory.Precoverage.Generates.toGrothendieck_eqproof · cited by 1
- CategoryTheory.topology_eq_iff_same_sheavesproof · cited by 0