Theorems · Definition · category theory

CategoryTheory.Prod.symmetry

(C : Type u₁) →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    (D : Type u₂) →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        (CategoryTheory.Prod.swap C D).comp (CategoryTheory.Prod.swap D C) ≅ CategoryTheory.Functor.id (C × D)

Swapping the factors of a Cartesian product of categories twice is naturally isomorphic to the identity functor.

Defined in

Mathlib.CategoryTheory.Products.Basic

Cited by

2 results in Mathlib

Foundations

Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category