Theorems · Definition · category theory

CategoryTheory.Linear.homCongr

(k : Type u_1) →
  {C : Type u_2} →
    [inst : CategoryTheory.Category.{v_1, u_2} C] →
      [inst_1 : Semiring k] →
        [inst_2 : CategoryTheory.Preadditive C] →
          [inst_3 : CategoryTheory.Linear k C] → {X Y W Z : C} → (X ≅ Y) → (W ≅ Z) → (X ⟶ W) ≃ₗ[k] Y ⟶ Z

Given isomorphic objects X ≅ Y, W ≅ Z in a k-linear category, we have a k-linear isomorphism between Hom(X, W) and Hom(Y, Z).

Defined in

Mathlib.CategoryTheory.Linear.Basic

Cited by

2 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategorySemiringCategoryTheory.PreadditiveCategoryTheory.Linear