Theorems · Theorem · category theory

CategoryTheory.Localization.SmallHom.mk_comp_mk

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {W : CategoryTheory.MorphismProperty C} {X Y Z : C}
  [inst_1 : CategoryTheory.Localization.HasSmallLocalizedHom W X Y]
  [inst_2 : CategoryTheory.Localization.HasSmallLocalizedHom W Y Z]
  [inst_3 : CategoryTheory.Localization.HasSmallLocalizedHom W X Z] (f : X ⟶ Y) (g : Y ⟶ Z),
  (CategoryTheory.Localization.SmallHom.mk W f).comp (CategoryTheory.Localization.SmallHom.mk W g) =
    CategoryTheory.Localization.SmallHom.mk W (CategoryTheory.CategoryStruct.comp f g)

Defined in

Mathlib.CategoryTheory.Localization.SmallHom

Cited by

2 results in Mathlib

Foundations

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

Assumes

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