Theorems · Theorem · category theory

CategoryTheory.MonObj.mul_leftUnitor

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.MonoidalCategory C]
  [inst_2 : CategoryTheory.BraidedCategory C] {M : C} [inst_3 : CategoryTheory.MonObj M],
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.MonoidalCategory.tensorμ (CategoryTheory.MonoidalCategoryStruct.tensorUnit C) M
          (CategoryTheory.MonoidalCategoryStruct.tensorUnit C) M)
        (CategoryTheory.MonoidalCategoryStruct.tensorHom
          (CategoryTheory.MonoidalCategoryStruct.leftUnitor (CategoryTheory.MonoidalCategoryStruct.tensorUnit C)).hom
          CategoryTheory.MonObj.mul))
      (CategoryTheory.MonoidalCategoryStruct.leftUnitor M).hom =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategoryStruct.tensorHom (CategoryTheory.MonoidalCategoryStruct.leftUnitor M).hom
        (CategoryTheory.MonoidalCategoryStruct.leftUnitor M).hom)
      CategoryTheory.MonObj.mul

Defined in

Mathlib.CategoryTheory.Monoidal.Mon

Cited by

0 results in Mathlib

Foundations

Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.BraidedCategoryCategoryTheory.MonObj