Theorems · Theorem · category theory
CategoryTheory.Sieve.ext
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X : C} {R S : CategoryTheory.Sieve X},
(∀ ⦃Y : C⦄ (f : Y ⟶ X), R.arrows f ↔ S.arrows f) → R = S- Defined in
- Mathlib.CategoryTheory.Sites.Sieves
- Cited by
- 43 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses propext, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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.Sievestatement and proof · cited by 552
- CategoryTheory.Sieve.arrowsstatement and proof · cited by 446
- CategoryTheory.Sieve.arrows_extproof · cited by 5
Cited by43
Results whose statement or proof uses this declaration.
- CategoryTheory.Sieve.generate_map_eq_functorPushforwardproof · cited by 6
- CategoryTheory.Sieve.pullbackArrows_commproof · cited by 6
- CategoryTheory.classifier_isSheafproof · cited by 4
- CategoryTheory.Sieve.generateFamily_eqproof · cited by 2
- CategoryTheory.Sieve.generateSingleton_eqproof · cited by 2
- CategoryTheory.PreOneHypercover.sieve₁_eq_pullback_sieve₁'proof · cited by 2
- CategoryTheory.Presheaf.comp_χ_eqproof · cited by 2
- CategoryTheory.Presheaf.equalizerSieve_self_eq_topproof · cited by 2
- CategoryTheory.Sieve.functorPullback_pullbackproof · cited by 2
- CategoryTheory.Sieve.functorPushforward_compproof · cited by 2
- CategoryTheory.Sieve.functorPushforward_functorproof · cited by 2
- CategoryTheory.Sieve.functorPushforward_over_mapproof · cited by 1