Theorems · Definition · category theory

CategoryTheory.GrothendieckTopology.Cover.Arrow.Y

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

The source of the arrow.

Defined in: Mathlib.CategoryTheory.Sites.Grothendieck
Cited by: 78 results in Mathlib
Foundations: Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category

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Cites4

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

CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.GrothendieckTopologystatement and proof · cited by 1,415
CategoryTheory.GrothendieckTopology.Coverstatement and proof · cited by 211
CategoryTheory.GrothendieckTopology.Cover.Arrowstatement and proof · cited by 99

Cited by112

Results whose statement or proof uses this declaration.

CategoryTheory.GrothendieckTopology.Cover.indexproof · cited by 142
CategoryTheory.GrothendieckTopology.Cover.Arrow.fstatement · cited by 45
CategoryTheory.GrothendieckTopology.Cover.Arrow.Relation.g₁statement · cited by 28
CategoryTheory.GrothendieckTopology.Cover.Arrow.Relation.g₂statement · cited by 27
CategoryTheory.Functor.IsDenseSubsite.mapPreimageproof · cited by 23
CategoryTheory.Meqproof · cited by 17
CategoryTheory.GrothendieckTopology.Cover.Arrow.hfstatement · cited by 15
CategoryTheory.Presheaf.IsSheaf.hom_extstatement · cited by 14
CategoryTheory.Functor.OneHypercoverDenseData.essSurj.restrictionproof · cited by 12
CategoryTheory.GrothendieckTopology.diagramNatTransproof · cited by 12
CategoryTheory.GrothendieckTopology.Cover.Arrow.mapproof · cited by 11
CategoryTheory.GrothendieckTopology.Cover.preOneHypercoverproof · cited by 10