Theorems · Theorem · category theory

CategoryTheory.Localization.SmallHom.comp_assoc

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {W : CategoryTheory.MorphismProperty C} {X Y Z T : C}
  [inst_1 : CategoryTheory.Localization.HasSmallLocalizedHom W X Y]
  [inst_2 : CategoryTheory.Localization.HasSmallLocalizedHom W X Z]
  [inst_3 : CategoryTheory.Localization.HasSmallLocalizedHom W X T]
  [inst_4 : CategoryTheory.Localization.HasSmallLocalizedHom W Y Z]
  [inst_5 : CategoryTheory.Localization.HasSmallLocalizedHom W Y T]
  [inst_6 : CategoryTheory.Localization.HasSmallLocalizedHom W Z T] (α : CategoryTheory.Localization.SmallHom W X Y)
  (β : CategoryTheory.Localization.SmallHom W Y Z) (γ : CategoryTheory.Localization.SmallHom W Z T),
  (α.comp β).comp γ = α.comp (β.comp γ)

Defined in

Mathlib.CategoryTheory.Localization.SmallHom

Cited by

1 results in Mathlib

Foundations

Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Localization.HasSmallLocalizedHomCategoryTheory.Localization.HasSmallLocalizedHomCategoryTheory.Localization.HasSmallLocalizedHomCategoryTheory.Localization.HasSmallLocalizedHomCategoryTheory.Localization.HasSmallLocalizedHomCategoryTheory.Localization.HasSmallLocalizedHom