Theorems · Theorem · category theory

CategoryTheory.Bicategory.conjugateEquiv_symm_apply

∀ {B : Type u} [inst : CategoryTheory.Bicategory B] {c d : B} {l₁ l₂ : c ⟶ d} {r₁ r₂ : d ⟶ c}
  (adj₁ : CategoryTheory.Bicategory.Adjunction l₁ r₁) (adj₂ : CategoryTheory.Bicategory.Adjunction l₂ r₂) (α : r₁ ⟶ r₂),
  (CategoryTheory.Bicategory.conjugateEquiv adj₁ adj₂).symm α =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.leftUnitor l₂).inv
      (CategoryTheory.CategoryStruct.comp
        ((CategoryTheory.Bicategory.mateEquiv adj₁ adj₂).symm
          (CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.rightUnitor r₁).hom
            (CategoryTheory.CategoryStruct.comp α (CategoryTheory.Bicategory.leftUnitor r₂).inv)))
        (CategoryTheory.Bicategory.rightUnitor l₁).hom)

Defined in

Mathlib.CategoryTheory.Bicategory.Adjunction.Mate

Cited by

2 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Bicategory