Theorems · Theorem · category theory
CategoryTheory.Sieve.exists_eq_ofArrows
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X : C} (R : CategoryTheory.Sieve X),
∃ I Y f, R = CategoryTheory.Sieve.ofArrows Y f- Defined in
- Mathlib.CategoryTheory.Sites.Sieves
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 31 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.
Cites10
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 · cited by 32,603
- CategoryTheory.ObjectProperty.FullSubcategory.objproof · cited by 1,316
- CategoryTheory.Sievestatement and proof · cited by 552
- CategoryTheory.Over.leftproof · cited by 541
- CategoryTheory.Sieve.arrowsproof · cited by 446
- CategoryTheory.Over.homproof · cited by 370
- CategoryTheory.Sieve.ofArrowsstatement · cited by 55
- CategoryTheory.Presieve.categoryproof · cited by 38
- CategoryTheory.Sieve.ofArrows_categoryproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- CategoryTheory.CoverPreserving.of_isContinuousproof · cited by 2
- CategoryTheory.Presieve.isSheafFor_over_map_op_comp_iffproof · cited by 1
- CategoryTheory.Presieve.isSheafFor_pullback_iffproof · cited by 1
- AlgebraicGeometry.Scheme.isConservative_pointSmallEtaleproof · cited by 1
- CategoryTheory.ObjectProperty.IsConservativeFamilyOfPoints.overproof · cited by 0