Theorems · Theorem · category theory

CategoryTheory.unit_conjugateEquiv

∀ {C : Type u₁} {D : Type u₂} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  {L₁ L₂ : CategoryTheory.Functor C D} {R₁ R₂ : CategoryTheory.Functor D C} (adj₁ : L₁ ⊣ R₁) (adj₂ : L₂ ⊣ R₂)
  (α : L₂ ⟶ L₁) (c : C),
  CategoryTheory.CategoryStruct.comp (adj₁.unit.app c) (((CategoryTheory.conjugateEquiv adj₁ adj₂) α).app (L₁.obj c)) =
    CategoryTheory.CategoryStruct.comp (adj₂.unit.app c) (R₂.map (α.app c))

A component of a transposed form of the conjugation definition.

Defined in

Mathlib.CategoryTheory.Adjunction.Mates

Cited by

2 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Category