Theorems · Theorem · category theory

CategoryTheory.MonoidalCategory.tensor_left_unitality

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.MonoidalCategory C]
  [inst_2 : CategoryTheory.BraidedCategory C] (X₁ X₂ : C),
  (CategoryTheory.MonoidalCategoryStruct.leftUnitor (CategoryTheory.MonoidalCategoryStruct.tensorObj X₁ X₂)).hom =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategoryStruct.whiskerRight
        (CategoryTheory.MonoidalCategoryStruct.leftUnitor (CategoryTheory.MonoidalCategoryStruct.tensorUnit C)).inv
        (CategoryTheory.MonoidalCategoryStruct.tensorObj X₁ X₂))
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.MonoidalCategory.tensorμ (CategoryTheory.MonoidalCategoryStruct.tensorUnit C)
          (CategoryTheory.MonoidalCategoryStruct.tensorUnit C) X₁ X₂)
        (CategoryTheory.MonoidalCategoryStruct.tensorHom (CategoryTheory.MonoidalCategoryStruct.leftUnitor X₁).hom
          (CategoryTheory.MonoidalCategoryStruct.leftUnitor X₂).hom))

Defined in

Mathlib.CategoryTheory.Monoidal.Braided.Basic

Cited by

3 results in Mathlib

Foundations

Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.BraidedCategory