Theorems · Theorem · category theory

CategoryTheory.Bicategory.mateEquiv_vcomp

∀ {B : Type u} [inst : CategoryTheory.Bicategory B] {a b c d e f : B} {g₁ : a ⟶ c} {g₂ : c ⟶ e} {h₁ : b ⟶ d}
  {h₂ : d ⟶ f} {l₁ : a ⟶ b} {r₁ : b ⟶ a} {l₂ : c ⟶ d} {r₂ : d ⟶ c} {l₃ : e ⟶ f} {r₃ : f ⟶ e}
  (adj₁ : CategoryTheory.Bicategory.Adjunction l₁ r₁) (adj₂ : CategoryTheory.Bicategory.Adjunction l₂ r₂)
  (adj₃ : CategoryTheory.Bicategory.Adjunction l₃ r₃)
  (α : CategoryTheory.CategoryStruct.comp g₁ l₂ ⟶ CategoryTheory.CategoryStruct.comp l₁ h₁)
  (β : CategoryTheory.CategoryStruct.comp g₂ l₃ ⟶ CategoryTheory.CategoryStruct.comp l₂ h₂),
  (CategoryTheory.Bicategory.mateEquiv adj₁ adj₃) (CategoryTheory.Bicategory.leftAdjointSquare.vcomp α β) =
    CategoryTheory.Bicategory.rightAdjointSquare.vcomp ((CategoryTheory.Bicategory.mateEquiv adj₁ adj₂) α)
      ((CategoryTheory.Bicategory.mateEquiv adj₂ adj₃) β)

The mates equivalence commutes with vertical composition.

Defined in

Mathlib.CategoryTheory.Bicategory.Adjunction.Mate

Cited by

4 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Bicategory