Theorems · Theorem · category theory

CategoryTheory.GrpObj.mul_inv_rev_assoc

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
  [inst_2 : CategoryTheory.BraidedCategory C] (G : C) [inst_3 : CategoryTheory.GrpObj G] {Z : C} (h : G ⟶ Z),
  CategoryTheory.CategoryStruct.comp CategoryTheory.MonObj.mul
      (CategoryTheory.CategoryStruct.comp CategoryTheory.GrpObj.inv h) =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategoryStruct.tensorHom CategoryTheory.GrpObj.inv CategoryTheory.GrpObj.inv)
      (CategoryTheory.CategoryStruct.comp (β_ G G).hom (CategoryTheory.CategoryStruct.comp CategoryTheory.MonObj.mul h))

Defined in

Mathlib.CategoryTheory.Monoidal.Grp

Cited by

0 results in Mathlib

Foundations

Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.BraidedCategoryCategoryTheory.GrpObj