Theorems · Theorem · category theory

CategoryTheory.Presieve.IsSheaf.isSeparated

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {J : CategoryTheory.GrothendieckTopology C}
  {P : CategoryTheory.Functor Cᵒᵖ (Type w)},
  CategoryTheory.Presieve.IsSheaf J P → CategoryTheory.Presieve.IsSeparated J P

Defined in: Mathlib.CategoryTheory.Sites.SheafOfTypes
Cited by: 8 results in Mathlib
Foundations: Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category

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Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites9

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
CategoryTheory.Functorstatement and proof · cited by 16,252
Oppositestatement and proof · cited by 8,081
CategoryTheory.GrothendieckTopologystatement and proof · cited by 1,415
CategoryTheory.Sieveproof · cited by 552
CategoryTheory.Presieve.IsSheafstatement and proof · cited by 66
CategoryTheory.Presieve.IsSheafFor.isSeparatedForproof · cited by 29
CategoryTheory.Presieve.IsSeparatedstatement · cited by 9

Cited by8

Results whose statement or proof uses this declaration.

CategoryTheory.Sheaf.isSeparatedproof · cited by 8
CategoryTheory.Functor.isContinuous_of_coverPreservingproof · cited by 4
CategoryTheory.Subfunctor.sheafify_isSheafproof · cited by 2
CategoryTheory.GrothendieckTopology.OneHypercover.isStronglySheafForproof · cited by 2
CategoryTheory.Presheaf.FamilyOfElementsOnObjects.IsCompatible.existsUnique_sectionproof · cited by 1
CategoryTheory.Sheaf.isLocallyInjective_iff_injectiveproof · cited by 1
CategoryTheory.GrothendieckTopology.CoversTop.sections_extproof · cited by 1
CategoryTheory.Pseudofunctor.DescentData.faithful_pullFunctorproof · cited by 0