Theorems · Definition · category theory

CategoryTheory.Iso.homCongr

{C : Type u} → [inst : CategoryTheory.Category.{v, u} C] → {X Y X₁ Y₁ : C} → (X ≅ X₁) → (Y ≅ Y₁) → (X ⟶ Y) ≃ (X₁ ⟶ Y₁)

If X is isomorphic to X₁ and Y is isomorphic to Y₁, then there is a natural bijection between X ⟶ Y and X₁ ⟶ Y₁. See also Equiv.arrowCongr.

Defined in

Mathlib.CategoryTheory.HomCongr

Cited by

30 results in Mathlib

Foundations

Depth 10 from the axioms · uses Quot.sound

Assumes

CategoryTheory.Category