Theorems · Theorem · category theory
CategoryTheory.Sieve.le_generate
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X : C} (R : CategoryTheory.Presieve X),
R ≤ (CategoryTheory.Sieve.generate R).arrows- Defined in
- Mathlib.CategoryTheory.Sites.Sieves
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 29 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.
Cites7
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
- CategoryTheory.Presievestatement and proof · cited by 449
- CategoryTheory.Sieve.arrowsstatement · cited by 446
- GaloisInsertion.gcproof · cited by 137
- CategoryTheory.Sieve.generatestatement · cited by 117
- GaloisConnection.le_u_lproof · cited by 52
- CategoryTheory.Sieve.giGenerateproof · cited by 7
Cited by21
Results whose statement or proof uses this declaration.
- CategoryTheory.Presieve.isSheafFor_iff_generateproof · cited by 20
- CategoryTheory.Sieve.pullbackArrows_commproof · cited by 6
- CategoryTheory.Presieve.isSeparatedFor_iff_generateproof · cited by 4
- CategoryTheory.Presieve.restrict_extendstatement · cited by 3
- CategoryTheory.Precoverage.locallyCoverDense_of_map_functorPullback_memproof · cited by 2
- CategoryTheory.Presieve.compatibleEquivGenerateSieveCompatibleproof · cited by 2
- CategoryTheory.Presieve.extend_restrictstatement and proof · cited by 2
- CategoryTheory.Presieve.map_le_functorPushforwardproof · cited by 1
- CategoryTheory.PreZeroHypercover.Hom.sieve₀_le_sieve₀proof · cited by 1
- CategoryTheory.Sieve.overEquiv_symm_generateproof · cited by 1
- CategoryTheory.coherentTopology.isSheaf_yoneda_objproof · cited by 1