Theorems · Theorem · category theory

CategoryTheory.GrothendieckTopology.Point.comp_hom

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {J : CategoryTheory.GrothendieckTopology C}
  {Φ₁ Φ₂ Φ₃ : J.Point} (f : Φ₁ ⟶ Φ₂) (g : Φ₂ ⟶ Φ₃),
  (CategoryTheory.CategoryStruct.comp f g).hom = CategoryTheory.CategoryStruct.comp g.hom f.hom

Defined in: Mathlib.CategoryTheory.Sites.Point.Category
Cited by: 1 results in Mathlib
Foundations: Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category

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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.compstatement · cited by 17,999
CategoryTheory.Functorstatement · cited by 16,252
CategoryTheory.GrothendieckTopologystatement and proof · cited by 1,415
CategoryTheory.GrothendieckTopology.Pointstatement and proof · cited by 123
CategoryTheory.GrothendieckTopology.Point.fiberstatement · cited by 93
CategoryTheory.GrothendieckTopology.Point.Hom.homstatement · cited by 12

Cited by1

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CategoryTheory.GrothendieckTopology.Point.comp_hom_assocproof · cited by 0