Theorems · Theorem · category theory

CategoryTheory.Bicategory.conjugateEquiv_comm

∀ {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 : l₂ ⟶ l₁}
  {β : l₁ ⟶ l₂},
  CategoryTheory.CategoryStruct.comp β α = CategoryTheory.CategoryStruct.id l₁ →
    CategoryTheory.CategoryStruct.comp ((CategoryTheory.Bicategory.conjugateEquiv adj₁ adj₂) α)
        ((CategoryTheory.Bicategory.conjugateEquiv adj₂ adj₁) β) =
      CategoryTheory.CategoryStruct.id r₁

Defined in

Mathlib.CategoryTheory.Bicategory.Adjunction.Mate

Cited by

0 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Bicategory