Theorems · Theorem · category theory

CategoryTheory.MonoidalCategory.leftUnitor_whiskerRight

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.MonoidalCategory C] (X Y : C),
  CategoryTheory.MonoidalCategoryStruct.whiskerRight (CategoryTheory.MonoidalCategoryStruct.leftUnitor X).hom Y =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategoryStruct.associator (CategoryTheory.MonoidalCategoryStruct.tensorUnit C) X Y).hom
      (CategoryTheory.MonoidalCategoryStruct.leftUnitor (CategoryTheory.MonoidalCategoryStruct.tensorObj X Y)).hom

We state it as a simp lemma, which is regarded as an involved version of id_whiskerRight X Y : 𝟙 X ▷ Y = 𝟙 (X ⊗ Y).

Defined in

Mathlib.CategoryTheory.Monoidal.Category

Cited by

9 results in Mathlib

Foundations

Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategory