Theorems · Definition · category theory
CategoryTheory.GrothendieckTopology.Cover.Arrow.precomp
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
{X : C} →
{J : CategoryTheory.GrothendieckTopology C} → {S : J.Cover X} → (I : S.Arrow) → {Z : C} → (Z ⟶ I.Y) → S.ArrowGiven I : S.Arrow and a morphism g : Z ⟶ I.Y, this is the arrow in S.Arrow
corresponding to g ≫ I.f.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- 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
- CategoryTheory.GrothendieckTopology.Cover.Arrow.Ystatement and proof · cited by 78
- CategoryTheory.GrothendieckTopology.Cover.Arrow.fproof · cited by 45
Cited by7
Results whose statement or proof uses this declaration.
- CategoryTheory.GrothendieckTopology.Cover.Arrow.precompRelationstatement and proof · cited by 4
- CategoryTheory.GrothendieckTopology.Plus.toPlus_applyproof · cited by 1
- CategoryTheory.GrothendieckTopology.Cover.Arrow.precompRelation_g₂statement · cited by 0
- CategoryTheory.GrothendieckTopology.Cover.Arrow.precomp_Ystatement and proof · cited by 0
- CategoryTheory.GrothendieckTopology.Cover.Arrow.precomp_fstatement and proof · cited by 0
- CategoryTheory.GrothendieckTopology.Cover.Arrow.precompRelation_Zstatement · cited by 0
- CategoryTheory.GrothendieckTopology.Cover.Arrow.precompRelation_g₁statement · cited by 0