Theorems · Theorem · category theory

CategoryTheory.LocalizerMorphism.smallHomMap_mk

∀ {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 : C₁}
  [inst_2 : CategoryTheory.Localization.HasSmallLocalizedHom W₁ X Y]
  [inst_3 : CategoryTheory.Localization.HasSmallLocalizedHom W₂ (Φ.functor.obj X) (Φ.functor.obj Y)] (f : X ⟶ Y),
  Φ.smallHomMap (CategoryTheory.Localization.SmallHom.mk W₁ f) =
    CategoryTheory.Localization.SmallHom.mk W₂ (Φ.functor.map f)

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.HasSmallLocalizedHom