Theorems · Theorem · category theory

CategoryTheory.Bicategory.mateEquiv_conjugateEquiv_vcomp

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

The mates equivalence commutes with this composition, essentially by mateEquiv_vcomp.

Defined in

Mathlib.CategoryTheory.Bicategory.Adjunction.Mate

Cited by

0 results in Mathlib

Foundations

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

Assumes

CategoryTheory.Bicategory