Theorems · Theorem · category theory

CategoryTheory.HopfObj.antipode_left_assoc

∀ {C : Type u₁} {inst : CategoryTheory.Category.{v₁, u₁} C} {inst_1 : CategoryTheory.MonoidalCategory C}
  {inst_2 : CategoryTheory.BraidedCategory C} (X : C) [self : CategoryTheory.HopfObj X] {Z : C} (h : X ⟶ Z),
  CategoryTheory.CategoryStruct.comp CategoryTheory.ComonObj.comul
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.MonoidalCategoryStruct.whiskerRight CategoryTheory.HopfObj.antipode X)
        (CategoryTheory.CategoryStruct.comp CategoryTheory.MonObj.mul h)) =
    CategoryTheory.CategoryStruct.comp CategoryTheory.ComonObj.counit
      (CategoryTheory.CategoryStruct.comp CategoryTheory.MonObj.one h)

Defined in

Mathlib.CategoryTheory.Monoidal.Hopf_

Cited by

2 results in Mathlib

Foundations

Depth 6 from the axioms · uses Quot.sound

Assumes

CategoryTheory.HopfObj