Theorems · Theorem · category theory

CategoryTheory.Bicategory.conjugateEquiv_symm_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 : r₁ ⟶ r₂}
  {β : r₂ ⟶ r₁},
  CategoryTheory.CategoryStruct.comp α β = CategoryTheory.CategoryStruct.id r₁ →
    CategoryTheory.CategoryStruct.comp ((CategoryTheory.Bicategory.conjugateEquiv adj₂ adj₁).symm β)
        ((CategoryTheory.Bicategory.conjugateEquiv adj₁ adj₂).symm α) =
      CategoryTheory.CategoryStruct.id l₁

Defined in

Mathlib.CategoryTheory.Bicategory.Adjunction.Mate

Cited by

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Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Bicategory