Theorems · Definition · category theory
CategoryTheory.Sieve.generate
{C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] → {X : C} → CategoryTheory.Presieve X → CategoryTheory.Sieve XGenerate the smallest sieve containing the given presieve.
- Defined in
- Mathlib.CategoryTheory.Sites.Sieves
- Cited by
- 117 results in Mathlib
- Foundations
- Depth 6 from the axioms, rests on 19 definitions · uses propext
- 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.Homproof · cited by 32,603
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Sievestatement · cited by 552
- CategoryTheory.Presievestatement and proof · cited by 449
Cited by138
Results whose statement or proof uses this declaration.
- CategoryTheory.Sieve.ofArrowsproof · cited by 55
- CategoryTheory.Presieve.isSheafFor_iff_generatestatement and proof · cited by 20
- CategoryTheory.Sieve.le_generatestatement · cited by 20
- CategoryTheory.Sieve.generate_sievestatement · cited by 19
- CategoryTheory.Sieve.generate_le_iffstatement and proof · cited by 16
- CategoryTheory.GrothendieckTopology.toPrecoverageproof · cited by 12
- CategoryTheory.Precoverage.generate_mem_toGrothendieckstatement · cited by 12
- CategoryTheory.Presieve.FamilyOfElements.sieveExtendstatement and proof · cited by 12
- CategoryTheory.Presieve.isSheaf_coverageproof · cited by 8
- TopCat.Presheaf.generateEquivalenceOpensLe_inverse'statement · cited by 7
- CategoryTheory.Sieve.giGeneratestatement and proof · cited by 7
- TopCat.Presheaf.generateEquivalenceOpensLestatement · cited by 6