Theorems · Theorem · category theory

CategoryTheory.Localization.Preadditive.homEquiv_symm_apply

∀ {C : Type u_1} {D : Type u_2} [inst : CategoryTheory.Category.{v_1, u_1} C]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} D] {L : CategoryTheory.Functor C D} {X Y : C} {X' Y' : D}
  (eX : L.obj X ≅ X') (eY : L.obj Y ≅ Y') (g : L.obj X ⟶ L.obj Y),
  (CategoryTheory.Localization.Preadditive.homEquiv eX eY).symm g =
    CategoryTheory.CategoryStruct.comp eX.inv (CategoryTheory.CategoryStruct.comp g eY.hom)

Defined in

Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive

Cited by

3 results in Mathlib

Foundations

Depth 14 from the axioms · uses propext, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category