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Theorems · Theorem · category theory

CategoryTheory.GrothendieckTopology.Cover.Arrow.hf

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X : C} {J : CategoryTheory.GrothendieckTopology C}
  {S : J.Cover X} (self : S.Arrow), (↑S).arrows self.f

The given arrow is contained in the given sieve.

Defined in
Mathlib.CategoryTheory.Sites.Grothendieck
Cited by
15 results in Mathlib
Foundations
Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.Category
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CategoryTheory.Presheaf.IsSheaf.amalgamate_map · cited by 6IsSheaf.amalgamate_mapCategoryTheory.Presheaf.isSheaf_iff_multifork · cited by 5Presheaf.isSheaf_iff_mult…CategoryTheory.Functor.OneHypercoverDenseData.essSurj.restriction_map · cited by 3essSurj.restriction_mapCategoryTheory.GrothendieckTopology.Plus.eq_mk_iff_exists · cited by 2Plus.eq_mk_iff_existsCategoryTheory.RanIsSheafOfIsCocontinuous.liftAux_map · cited by 2RanIsSheafOfIsCocontinuou…CategoryTheory.GrothendieckTopology.Plus.res_mk_eq_mk_pullback · cited by 2Plus.res_mk_eq_mk_pullbackCategoryTheory.GrothendieckTopology.Cover.Arrow.middle_spec · cited by 2Arrow.middle_specCategoryTheory.Sheaf.isIso_of_coversTop · cited by 1Sheaf.isIso_of_coversTopCategoryTheory.GrothendieckTopology.Cover.Arrow.to_middle_condition · cited by 0Arrow.to_middle_conditionCategoryTheory.GrothendieckTopology.Cover.preOneHypercover_sieve₀ · cited by 0Cover.preOneHypercover_si…CategoryTheory.Meq.pullback_apply · cited by 0Meq.pullback_applyCategoryTheory.Meq.refine_apply · cited by 0Meq.refine_applyCategoryTheory.Functor.IsDenseSubsite.isIso_ranCounit_app_of_isDenseSubsite · cited by 0IsDenseSubsite.isIso_ranC…CategoryTheory.GrothendieckTopology.Plus.exists_of_sep · cited by 0Plus.exists_of_sepCategoryTheory.GrothendieckTopology.Cover.Arrow.from_middle_condition · cited by 0Arrow.from_middle_conditi…DFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.GrothendieckTopology · cited by 1415CategoryTheory.Grothendie…CategoryTheory.Sieve · cited by 552CategoryTheory.SieveCategoryTheory.Sieve.arrows · cited by 446Sieve.arrowsCategoryTheory.GrothendieckTopology.Cover · cited by 211GrothendieckTopology.CoverCategoryTheory.GrothendieckTopology.Cover.Arrow · cited by 99Cover.ArrowCategoryTheory.GrothendieckTopology.Cover.Arrow.Y · cited by 78Arrow.YCategoryTheory.GrothendieckTopology.Cover.Arrow.f · cited by 45Arrow.fArrow.hfCITED BYCITES

Cites10

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Cited by15

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