Theorems · Theorem · category theory

CategoryTheory.LocalizerMorphism.smallHomMap_comp

∀ {C₁ : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C₁] {W₁ : CategoryTheory.MorphismProperty C₁} {C₂ : Type u₂}
  [inst_1 : CategoryTheory.Category.{v₂, u₂} C₂] {W₂ : CategoryTheory.MorphismProperty C₂}
  (Φ : CategoryTheory.LocalizerMorphism W₁ W₂) {X Y Z : C₁}
  [inst_2 : CategoryTheory.Localization.HasSmallLocalizedHom W₁ X Y]
  [inst_3 : CategoryTheory.Localization.HasSmallLocalizedHom W₁ Y Z]
  [inst_4 : CategoryTheory.Localization.HasSmallLocalizedHom W₁ X Z]
  [inst_5 : CategoryTheory.Localization.HasSmallLocalizedHom W₂ (Φ.functor.obj X) (Φ.functor.obj Y)]
  [inst_6 : CategoryTheory.Localization.HasSmallLocalizedHom W₂ (Φ.functor.obj Y) (Φ.functor.obj Z)]
  [inst_7 : CategoryTheory.Localization.HasSmallLocalizedHom W₂ (Φ.functor.obj X) (Φ.functor.obj Z)]
  (f : CategoryTheory.Localization.SmallHom W₁ X Y) (g : CategoryTheory.Localization.SmallHom W₁ Y Z),
  Φ.smallHomMap (f.comp g) = (Φ.smallHomMap f).comp (Φ.smallHomMap g)

Defined in

Mathlib.CategoryTheory.Localization.SmallHom

Cited by

1 results in Mathlib

Foundations

Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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