Theorems · Inductive type · category theory
CategoryTheory.Precoverage.Saturate
{C : Type u_1} →
[inst : CategoryTheory.Category.{u_2, u_1} C] → CategoryTheory.Precoverage C → (X : C) → CategoryTheory.Sieve X → PropAn auxiliary definition used to define the Grothendieck topology associated to a precoverage.
See Precoverage.toGrothendieck.
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
- CategoryTheory.Sievestatement · cited by 552
- CategoryTheory.Precoveragestatement · cited by 204
Cited by14
Results whose statement or proof uses this declaration.
- CategoryTheory.Precoverage.toGrothendieckproof · cited by 41
- CategoryTheory.Precoverage.toGrothendieck_le_iff_le_toPrecoverageproof · cited by 4
- CategoryTheory.Functor.coverPreserving_restrictedTopologyproof · cited by 3
- CategoryTheory.Precoverage.isSheaf_toGrothendieck_iffproof · cited by 2
- CategoryTheory.Precoverage.Saturate.belowstatement · cited by 1
- CategoryTheory.Precoverage.toGrothendieck_eq_sInfproof · cited by 0
- CategoryTheory.Precoverage.Saturate.brecOnstatement and proof · cited by 0
- CategoryTheory.Precoverage.Saturate.casesOnstatement and proof · cited by 0
- CategoryTheory.Precoverage.Saturate.hcongr_5statement and proof · cited by 0
- CategoryTheory.Precoverage.Saturate.recOnstatement and proof · cited by 0
- CategoryTheory.Coverage.saturate_iff_saturate_toPrecoveragestatement and proof · cited by 0