Theorems · Definition · category theory

CategoryTheory.prod.prodFunctorToFunctorProdAssociator

(C : Type u₁) →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    (D : Type u₂) →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        (E : Type u₃) →
          [inst_2 : CategoryTheory.Category.{v₃, u₃} E] →
            (A : Type u₄) →
              [inst_3 : CategoryTheory.Category.{v₄, u₄} A] →
                (CategoryTheory.prod.associativity (CategoryTheory.Functor A C) (CategoryTheory.Functor A D)
                          (CategoryTheory.Functor A E)).functor.comp
                    (((CategoryTheory.Functor.id (CategoryTheory.Functor A C)).prod
                          (CategoryTheory.prodFunctorToFunctorProd A D E)).comp
                      (CategoryTheory.prodFunctorToFunctorProd A C (D × E))) ≅
                  ((CategoryTheory.prodFunctorToFunctorProd A C D).prod
                        (CategoryTheory.Functor.id (CategoryTheory.Functor A E))).comp
                    ((CategoryTheory.prodFunctorToFunctorProd A (C × D) E).comp
                      (CategoryTheory.prod.associativity C D E).congrRight.functor)

The associator isomorphism is compatible with prodFunctorToFunctorProd.

Defined in

Mathlib.CategoryTheory.Products.Associator

Cited by

2 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category