Theorems · Theorem · category theory
CategoryTheory.Presieve.compatible_iff_sieveCompatible
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {P : CategoryTheory.Functor Cᵒᵖ (Type w)} {X : C}
{S : CategoryTheory.Sieve X} (x : CategoryTheory.Presieve.FamilyOfElements P S.arrows),
x.Compatible ↔ x.SieveCompatible- Defined in
- Mathlib.CategoryTheory.Sites.IsSheafFor
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Functor.mapproof · cited by 8,698
- Oppositestatement and proof · cited by 8,081
- CategoryTheory.CategoryStruct.idproof · cited by 6,235
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- CategoryTheory.Category.id_compproof · cited by 1,998
- Quiver.Hom.opproof · cited by 1,948
- CategoryTheory.Functor.map_idproof · cited by 616
Cited by6
Results whose statement or proof uses this declaration.
- CategoryTheory.classifier_isSheafproof · cited by 4
- CategoryTheory.Presieve.extend_restrictproof · cited by 2
- CategoryTheory.Presieve.isSheafFor_bindproof · cited by 2
- CategoryTheory.Presheaf.subsingleton_iff_isSeparatedForproof · cited by 1
- CategoryTheory.Equalizer.Sieve.compatible_iffproof · cited by 0
- CategoryTheory.Presieve.FamilyOfElements.Compatible.to_sieveCompatibleproof · cited by 0