Theorems · Theorem · category theory
CategoryTheory.Sieve.generate_le_iff
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X : C} (R : CategoryTheory.Presieve X)
(S : CategoryTheory.Sieve X), CategoryTheory.Sieve.generate R ≤ S ↔ R ≤ S.arrows- Defined in
- Mathlib.CategoryTheory.Sites.Sieves
- Cited by
- 16 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.
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.Homproof · cited by 32,603
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.CategoryStruct.idproof · cited by 6,235
- CategoryTheory.Category.id_compproof · cited by 1,998
- CategoryTheory.Sievestatement and proof · cited by 552
- CategoryTheory.Presievestatement and proof · cited by 449
- CategoryTheory.Sieve.arrowsstatement and proof · cited by 446
- CategoryTheory.Sieve.generatestatement and proof · cited by 117
- CategoryTheory.Sieve.downward_closedproof · cited by 39
Cited by17
Results whose statement or proof uses this declaration.
- CategoryTheory.Sieve.giGenerateproof · cited by 7
- CategoryTheory.Sieve.ofArrows_category'proof · cited by 6
- CategoryTheory.Coverage.mem_toGrothendieck_sieves_of_supersetproof · cited by 2
- CategoryTheory.Sieve.overEquiv_generateproof · cited by 1
- CategoryTheory.Precoverage.ZeroHypercover.Hom.isSheafFor_iffproof · cited by 1
- CategoryTheory.PreZeroHypercover.Hom.sieve₀_le_sieve₀proof · cited by 1
- CategoryTheory.Sieve.overEquiv_symm_generateproof · cited by 1
- CategoryTheory.Sieve.generate_functorPullback_leproof · cited by 1
- CategoryTheory.Pretopology.toGrothendieck_toCoverageproof · cited by 1
- CategoryTheory.regularTopology.mem_sieves_of_hasEffectiveEpiproof · cited by 1
- CategoryTheory.Presieve.isSheaf_pretopologyproof · cited by 1