Theorems · Theorem · category theory

CategoryTheory.Center.whiskerRight_comm_assoc

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.MonoidalCategory C]
  {X₁ X₂ : CategoryTheory.Center C} (f : X₁ ⟶ X₂) (Y : CategoryTheory.Center C) (U : C) {Z : C}
  (h : CategoryTheory.MonoidalCategoryStruct.tensorObj U (X₂.tensorObj Y).fst ⟶ Z),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategoryStruct.whiskerRight (CategoryTheory.MonoidalCategoryStruct.whiskerRight f.f Y.fst)
        U)
      (CategoryTheory.CategoryStruct.comp ((X₂.tensorObj Y).snd.β U).hom h) =
    CategoryTheory.CategoryStruct.comp ((X₁.tensorObj Y).snd.β U).hom
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.MonoidalCategoryStruct.whiskerLeft U
          (CategoryTheory.MonoidalCategoryStruct.whiskerRight f.f Y.fst))
        h)

Defined in

Mathlib.CategoryTheory.Monoidal.Center

Cited by

0 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategory