Theorems · Inductive type · category theory
CategoryTheory.Precoverage.IsStableUnderComposition
{C : Type u} → [inst : CategoryTheory.Category.{v, u} C] → CategoryTheory.Precoverage C → PropA precoverage is stable under composition if the indexed composition
of coverings is again a covering.
Use Precoverage.comp_mem_coverings for less universe restrictions.
Note: This is stronger than the analogous requirement for a Pretopology, because
this is in general not equal to a Presieve.bind.
- Defined in
- Mathlib.CategoryTheory.Sites.Precoverage
- Cited by
- 23 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.
Cites2
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.Precoveragestatement · cited by 204
Cited by29
Results whose statement or proof uses this declaration.
- CategoryTheory.Precoverage.ZeroHypercover.bindstatement and proof · cited by 8
- CategoryTheory.Precoverage.toPretopologystatement and proof · cited by 6
- CategoryTheory.Precoverage.toGrothendieck_toPretopology_eq_toGrothendieckstatement and proof · cited by 4
- CategoryTheory.Precoverage.mem_toGrothendieck_iff_of_isStableUnderCompositionstatement and proof · cited by 3
- CategoryTheory.MorphismProperty.toGrothendieck_comap_forget_eq_restrictedTopologystatement and proof · cited by 2
- CategoryTheory.Precoverage.locallyCoverDense_of_map_functorPullback_memstatement and proof · cited by 2
- CategoryTheory.Precoverage.toGrothendieck_comap_eq_restrictedTopologystatement and proof · cited by 2
- CategoryTheory.Precoverage.ZeroHypercover.pushforwardstatement and proof · cited by 2
- CategoryTheory.MorphismProperty.locallyCoverDense_forget_of_lestatement and proof · cited by 2
- CategoryTheory.Pseudofunctor.IsPrestack.of_precoveragestatement and proof · cited by 1
- CategoryTheory.MorphismProperty.isContinuous_comap_forgetstatement and proof · cited by 1
- CategoryTheory.MorphismProperty.toGrothendieck_comap_forget_eq_inducedTopologystatement and proof · cited by 1