Theorems · Theorem · category theory

CategoryTheory.MonoidalCategory.associator_inv_naturality_middle_assoc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.MonoidalCategory C] (X : C) {Y Y' : C}
  (f : Y ⟶ Y') (Z : C) {Z_1 : C}
  (h : CategoryTheory.MonoidalCategoryStruct.tensorObj (CategoryTheory.MonoidalCategoryStruct.tensorObj X Y') Z ⟶ Z_1),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategoryStruct.whiskerLeft X (CategoryTheory.MonoidalCategoryStruct.whiskerRight f Z))
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.associator X Y' Z).inv h) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.associator X Y Z).inv
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.MonoidalCategoryStruct.whiskerRight (CategoryTheory.MonoidalCategoryStruct.whiskerLeft X f) Z)
        h)

Defined in

Mathlib.CategoryTheory.Monoidal.Category

Cited by

7 results in Mathlib

Foundations

Depth 9 from the axioms · uses propext, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategory