Theorems · Theorem · category theory

CategoryTheory.NatTrans.IsMonoidal.tensor_assoc

∀ {C : Type u₁} {inst : CategoryTheory.Category.{v₁, u₁} C} {inst_1 : CategoryTheory.MonoidalCategory C} {D : Type u₂}
  {inst_2 : CategoryTheory.Category.{v₂, u₂} D} {inst_3 : CategoryTheory.MonoidalCategory D}
  {F₁ F₂ : CategoryTheory.Functor C D} {τ : F₁ ⟶ F₂} {inst_4 : F₁.LaxMonoidal} {inst_5 : F₂.LaxMonoidal}
  [self : CategoryTheory.NatTrans.IsMonoidal τ] (X Y : C) {Z : D}
  (h : F₂.obj (CategoryTheory.MonoidalCategoryStruct.tensorObj X Y) ⟶ Z),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Functor.LaxMonoidal.μ F₁ X Y)
      (CategoryTheory.CategoryStruct.comp (τ.app (CategoryTheory.MonoidalCategoryStruct.tensorObj X Y)) h) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.tensorHom (τ.app X) (τ.app Y))
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Functor.LaxMonoidal.μ F₂ X Y) h)

Defined in

Mathlib.CategoryTheory.Monoidal.NaturalTransformation

Cited by

0 results in Mathlib

Foundations

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

Assumes

CategoryTheory.NatTrans.IsMonoidal