Theorems · Theorem · category theory

CategoryTheory.Dial.associator_naturality

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasFiniteProducts C]
  [inst_2 : CategoryTheory.Limits.HasPullbacks C] {X₁ X₂ X₃ Y₁ Y₂ Y₃ : CategoryTheory.Dial C} (f₁ : X₁ ⟶ Y₁)
  (f₂ : X₂ ⟶ Y₂) (f₃ : X₃ ⟶ Y₃),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategoryStruct.tensorHom (CategoryTheory.MonoidalCategoryStruct.tensorHom f₁ f₂) f₃)
      (CategoryTheory.MonoidalCategoryStruct.associator Y₁ Y₂ Y₃).hom =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.associator X₁ X₂ X₃).hom
      (CategoryTheory.MonoidalCategoryStruct.tensorHom f₁ (CategoryTheory.MonoidalCategoryStruct.tensorHom f₂ f₃))

Defined in

Mathlib.CategoryTheory.Dialectica.Monoidal

Cited by

0 results in Mathlib

Foundations

Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasFiniteProductsCategoryTheory.Limits.HasPullbacks