Theorems · Theorem · category theory

CategoryTheory.prod.functorProdToProdFunctorAssociator_hom_app

∀ (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] (X : CategoryTheory.Functor A ((C × D) × E)),
  (CategoryTheory.prod.functorProdToProdFunctorAssociator C D E A).hom.app X =
    CategoryTheory.Prod.mkHom
      (CategoryTheory.CategoryStruct.id
        ((X.comp (CategoryTheory.prod.associator C D E)).comp (CategoryTheory.Prod.fst C (D × E))))
      (CategoryTheory.Prod.mkHom
        (CategoryTheory.CategoryStruct.id
          (((X.comp (CategoryTheory.prod.associator C D E)).comp (CategoryTheory.Prod.snd C (D × E))).comp
            (CategoryTheory.Prod.fst D E)))
        (CategoryTheory.CategoryStruct.id
          (((X.comp (CategoryTheory.prod.associator C D E)).comp (CategoryTheory.Prod.snd C (D × E))).comp
            (CategoryTheory.Prod.snd D E))))

Defined in

Mathlib.CategoryTheory.Products.Associator

Cited by

0 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category