Mathlib Map

Theorems · Definition · algebraic geometry

CategoryTheory.MorphismProperty.precoverage

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] → CategoryTheory.MorphismProperty C → CategoryTheory.Precoverage C

This is the precoverage on C where covering presieves are those where every morphism satisfies P.

Defined in
Mathlib.CategoryTheory.Sites.MorphismProperty
Cited by
23 results in Mathlib
Foundations
Depth 4 from the axioms · uses no axioms
Assumes
CategoryTheory.Category

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AlgebraicGeometry.Scheme.precoverage · cited by 336Scheme.precoverageCategoryTheory.MorphismProperty.pretopology · cited by 8MorphismProperty.pretopol…AlgebraicGeometry.Scheme.precoverage_mono · cited by 7Scheme.precoverage_monoCategoryTheory.Precoverage.galoisConnection_morphismProperty_precoverage · cited by 5Precoverage.galoisConnect…TopCat.precoverage · cited by 3TopCat.precoverageCategoryTheory.MorphismProperty.toGrothendieck_comap_forget_eq_restrictedTopology · cited by 2MorphismProperty.toGrothe…CategoryTheory.MorphismProperty.coverage · cited by 2MorphismProperty.coverageCategoryTheory.MorphismProperty.precoverage_monotone · cited by 2MorphismProperty.precover…CategoryTheory.MorphismProperty.exists_map_eq_of_presieve · cited by 2MorphismProperty.exists_m…CategoryTheory.MorphismProperty.locallyCoverDense_forget_of_le · cited by 2MorphismProperty.locallyC…AlgebraicGeometry.Scheme.proetalePrecoverage_le_precoverage_weaklyEtale · cited by 1Scheme.proetalePrecoverag…CategoryTheory.MorphismProperty.bot_mem_precoverage · cited by 1MorphismProperty.bot_mem_…CategoryTheory.MorphismProperty.isContinuous_comap_forget · cited by 1MorphismProperty.isContin…CategoryTheory.MorphismProperty.toGrothendieck_comap_forget_eq_inducedTopology · cited by 1MorphismProperty.toGrothe…CategoryTheory.MorphismProperty.coverPreserving_comap_forget · cited by 1MorphismProperty.coverPre…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomSet.ofPred · cited by 6101Set.ofPredCategoryTheory.MorphismProperty · cited by 2179CategoryTheory.MorphismPr…CategoryTheory.Presieve · cited by 449CategoryTheory.PresieveCategoryTheory.Precoverage · cited by 204CategoryTheory.PrecoverageMorphismProperty.precoverageCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by27

Results whose statement or proof uses this declaration.