Theorems · Theorem · category theory
CategoryTheory.Presieve.ofArrows_pUnit
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X Y : C} (f : Y ⟶ X),
(CategoryTheory.Presieve.ofArrows (fun x => Y) fun x => f) = CategoryTheory.Presieve.singleton f- Defined in
- Mathlib.CategoryTheory.Sites.Sieves
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 27 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.
Cites6
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.Homstatement and proof · cited by 32,603
- CategoryTheory.Presievestatement and proof · cited by 449
- CategoryTheory.Presieve.ofArrowsstatement · cited by 150
- CategoryTheory.Presieve.singletonstatement and proof · cited by 57
- CategoryTheory.Presieve.ofArrows_of_uniqueproof · cited by 2
Cited by10
Results whose statement or proof uses this declaration.
- CategoryTheory.PreZeroHypercover.presieve₀_singletonproof · cited by 4
- CategoryTheory.Presieve.isSheafFor_singleton_iff_of_isoproof · cited by 1
- CategoryTheory.PreZeroHypercover.presieve₀_sigmaOfIsColimitproof · cited by 1
- CategoryTheory.PreZeroHypercover.mem_of_isoproof · cited by 1
- CategoryTheory.MorphismProperty.singleton_mem_precoverageproof · cited by 0
- AlgebraicGeometry.Scheme.Hom.singleton_mem_fppfPrecoverageproof · cited by 0
- CategoryTheory.Presieve.map_singletonproof · cited by 0
- CategoryTheory.regularTopology.isSheaf_yoneda_objproof · cited by 0
- AlgebraicGeometry.Scheme.singleton_mem_precoverage_iffproof · cited by 0
- CategoryTheory.Presieve.pushforward_singletonproof · cited by 0