Theorems · Definition · category theory

CategoryTheory.Localization.Preadditive.homEquiv

{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} → (L.obj X ≅ X') → (L.obj Y ≅ Y') → (X' ⟶ Y') ≃ (L.obj X ⟶ L.obj Y)

The bijection (X' ⟶ Y') ≃ (L.obj X ⟶ L.obj Y) induced by isomorphisms eX : L.obj X ≅ X' and eY : L.obj Y ≅ Y'.

Defined in

Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive

Cited by

5 results in Mathlib

Foundations

Depth 10 from the axioms · uses propext, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category