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Theorems · Definition · category theory

CategoryTheory.GrothendieckTopology.Cover.Arrow.f

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {X : C} → {J : CategoryTheory.GrothendieckTopology C} → {S : J.Cover X} → (self : S.Arrow) → self.Y ⟶ X

The arrow itself.

Defined in
Mathlib.CategoryTheory.Sites.Grothendieck
Cited by
45 results in Mathlib
Foundations
Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.Category
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CategoryTheory.GrothendieckTopology.Cover.Arrow.hf · cited by 15Arrow.hfCategoryTheory.Presheaf.IsSheaf.hom_ext · cited by 14IsSheaf.hom_extCategoryTheory.GrothendieckTopology.Cover.Arrow.map · cited by 11Arrow.mapCategoryTheory.GrothendieckTopology.Cover.preOneHypercover · cited by 10Cover.preOneHypercoverCategoryTheory.GrothendieckTopology.Cover.Arrow.base · cited by 6Arrow.baseCategoryTheory.Meq.refine · cited by 6Meq.refineCategoryTheory.GrothendieckTopology.Cover.Arrow.precomp · cited by 6Arrow.precompCategoryTheory.Presheaf.IsSheaf.amalgamate_map · cited by 6IsSheaf.amalgamate_mapCategoryTheory.GrothendieckTopology.toPlus_naturality · cited by 6GrothendieckTopology.toPl…CategoryTheory.GrothendieckTopology.Cover.toMultiequalizer · cited by 6Cover.toMultiequalizerCategoryTheory.Meq.mk · cited by 5Meq.mkCategoryTheory.Meq.pullback · cited by 5Meq.pullbackCategoryTheory.Presheaf.isSheaf_iff_multifork · cited by 5Presheaf.isSheaf_iff_mult…CategoryTheory.GrothendieckTopology.plusMap_toPlus · cited by 5GrothendieckTopology.plus…CategoryTheory.RanIsSheafOfIsCocontinuous.liftAux · cited by 5RanIsSheafOfIsCocontinuou…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.GrothendieckTopology · cited by 1415CategoryTheory.Grothendie…CategoryTheory.GrothendieckTopology.Cover · cited by 211GrothendieckTopology.CoverCategoryTheory.GrothendieckTopology.Cover.Arrow · cited by 99Cover.ArrowCategoryTheory.GrothendieckTopology.Cover.Arrow.Y · cited by 78Arrow.YArrow.fCITED BYCITES

Cites6

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Cited by61

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