Theorems · Definition · category theory

CategoryTheory.Iso.eHomCongr

(V : Type u') →
  [inst : CategoryTheory.Category.{v', u'} V] →
    [inst_1 : CategoryTheory.MonoidalCategory V] →
      {C : Type u} →
        [inst_2 : CategoryTheory.Category.{v, u} C] →
          [inst_3 : CategoryTheory.EnrichedOrdinaryCategory V C] →
            {X Y X₁ Y₁ : C} → (X ≅ X₁) → (Y ≅ Y₁) → ((X ⟶[V] Y) ≅ X₁ ⟶[V] Y₁)

Given isomorphisms α : X ≅ X₁ and β : Y ≅ Y₁ in C, we can construct an isomorphism between V objects X ⟶[V] Y and X₁ ⟶[V] Y₁.

Defined in

Mathlib.CategoryTheory.Enriched.HomCongr

Cited by

9 results in Mathlib

Foundations

Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.CategoryCategoryTheory.EnrichedOrdinaryCategory