Theorems · Theorem · category theory

CategoryTheory.Bimon.one_comul_assoc

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.MonoidalCategory C]
  [inst_2 : CategoryTheory.BraidedCategory C] (M : C) [inst_3 : CategoryTheory.BimonObj M] {Z : C}
  (h : CategoryTheory.MonoidalCategoryStruct.tensorObj M M ⟶ Z),
  CategoryTheory.CategoryStruct.comp CategoryTheory.MonObj.one
      (CategoryTheory.CategoryStruct.comp CategoryTheory.ComonObj.comul h) =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategoryStruct.leftUnitor (CategoryTheory.MonoidalCategoryStruct.tensorUnit C)).inv
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.MonoidalCategoryStruct.tensorHom CategoryTheory.MonObj.one CategoryTheory.MonObj.one) h)

Defined in

Mathlib.CategoryTheory.Monoidal.Bimon_

Cited by

1 results in Mathlib

Foundations

Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.BraidedCategoryCategoryTheory.BimonObj