Theorems · Theorem · category theory

CategoryTheory.Bicategory.conjugateEquiv_comp

∀ {B : Type u} [inst : CategoryTheory.Bicategory B] {c d : B} {l₁ l₂ l₃ : c ⟶ d} {r₁ r₂ r₃ : d ⟶ c}
  (adj₁ : CategoryTheory.Bicategory.Adjunction l₁ r₁) (adj₂ : CategoryTheory.Bicategory.Adjunction l₂ r₂)
  (adj₃ : CategoryTheory.Bicategory.Adjunction l₃ r₃) (α : l₂ ⟶ l₁) (β : l₃ ⟶ l₂),
  CategoryTheory.CategoryStruct.comp ((CategoryTheory.Bicategory.conjugateEquiv adj₁ adj₂) α)
      ((CategoryTheory.Bicategory.conjugateEquiv adj₂ adj₃) β) =
    (CategoryTheory.Bicategory.conjugateEquiv adj₁ adj₃) (CategoryTheory.CategoryStruct.comp β α)

Defined in

Mathlib.CategoryTheory.Bicategory.Adjunction.Mate

Cited by

2 results in Mathlib

Foundations

Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Bicategory