Theorems · Theorem · category theory

CategoryTheory.associativity_app_assoc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {M : Type u_1} [inst_1 : CategoryTheory.Category.{v_1, u_1} M]
  [inst_2 : CategoryTheory.MonoidalCategory M] (F : CategoryTheory.Functor M (CategoryTheory.Functor C C))
  (m₁ m₂ m₃ : M) (X : C) [inst_3 : F.LaxMonoidal] {Z : C}
  (h :
    (F.obj
            (CategoryTheory.MonoidalCategoryStruct.tensorObj m₁
              (CategoryTheory.MonoidalCategoryStruct.tensorObj m₂ m₃))).obj
        X ⟶
      Z),
  CategoryTheory.CategoryStruct.comp ((F.obj m₃).map ((CategoryTheory.Functor.LaxMonoidal.μ F m₁ m₂).app X))
      (CategoryTheory.CategoryStruct.comp
        ((CategoryTheory.Functor.LaxMonoidal.μ F (CategoryTheory.MonoidalCategoryStruct.tensorObj m₁ m₂) m₃).app X)
        (CategoryTheory.CategoryStruct.comp
          ((F.map (CategoryTheory.MonoidalCategoryStruct.associator m₁ m₂ m₃).hom).app X) h)) =
    CategoryTheory.CategoryStruct.comp ((CategoryTheory.Functor.LaxMonoidal.μ F m₂ m₃).app ((F.obj m₁).obj X))
      (CategoryTheory.CategoryStruct.comp
        ((CategoryTheory.Functor.LaxMonoidal.μ F m₁ (CategoryTheory.MonoidalCategoryStruct.tensorObj m₂ m₃)).app X) h)

Defined in

Mathlib.CategoryTheory.Monoidal.End

Cited by

1 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.Functor.LaxMonoidal