Theorems · Theorem · category theory
CategoryTheory.Precoverage.isSheaf_toGrothendieck_iff_of_isStableUnderBaseChange_of_small
∀ {C : Type u_2} [inst : CategoryTheory.Category.{v_1, u_2} C] {J : CategoryTheory.Precoverage C}
[J.IsStableUnderBaseChange] [J.HasPullbacks] [J.Small] (P : CategoryTheory.Functor Cᵒᵖ (Type u_1)),
CategoryTheory.Presieve.IsSheaf J.toGrothendieck P ↔
∀ ⦃X : C⦄ (E : J.ZeroHypercover X), CategoryTheory.Presieve.IsSheafFor P E.presieve₀- Defined in
- Mathlib.CategoryTheory.Sites.Coverage
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites33
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homproof · cited by 32,603
- CategoryTheory.Functorstatement and proof · cited by 16,252
- Oppositestatement and proof · cited by 8,081
- CategoryTheory.Sieveproof · cited by 552
- CategoryTheory.Precoverage.ZeroHypercover.toPreZeroHypercoverstatement and proof · cited by 469
- CategoryTheory.Presieveproof · cited by 449
- CategoryTheory.Sieve.arrowsproof · cited by 446
- CategoryTheory.PreZeroHypercoverproof · cited by 256
- CategoryTheory.Precoveragestatement and proof · cited by 204
- CategoryTheory.Precoverage.coveringsproof · cited by 194
- CategoryTheory.Presieve.IsSheafForstatement and proof · cited by 111
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.isSheaf_type_propQCTopology_iffproof · cited by 1