Theorems · Theorem · category theory

CategoryTheory.MonoidalCategory.associator_naturality_left_assoc

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

Defined in

Mathlib.CategoryTheory.Monoidal.Category

Cited by

2 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategory