Theorems · Theorem · category theory

CategoryTheory.unit_mateEquiv

∀ {C : Type u₁} {D : Type u₂} {E : Type u₃} {F : Type u₄} [inst : CategoryTheory.Category.{v₁, u₁} C]
  [inst_1 : CategoryTheory.Category.{v₂, u₂} D] [inst_2 : CategoryTheory.Category.{v₃, u₃} E]
  [inst_3 : CategoryTheory.Category.{v₄, u₄} F] {G : CategoryTheory.Functor C E} {H : CategoryTheory.Functor D F}
  {L₁ : CategoryTheory.Functor C D} {R₁ : CategoryTheory.Functor D C} {L₂ : CategoryTheory.Functor E F}
  {R₂ : CategoryTheory.Functor F E} (adj₁ : L₁ ⊣ R₁) (adj₂ : L₂ ⊣ R₂) (α : CategoryTheory.TwoSquare G L₁ L₂ H) (c : C),
  CategoryTheory.CategoryStruct.comp (G.map (adj₁.unit.app c))
      (((CategoryTheory.mateEquiv adj₁ adj₂) α).app (L₁.obj c)) =
    CategoryTheory.CategoryStruct.comp (adj₂.unit.app (G.obj ((CategoryTheory.Functor.id C).obj c)))
      (R₂.map (α.app ((CategoryTheory.Functor.id C).obj c)))

A component of a transposed version of the mates correspondence.

Defined in

Mathlib.CategoryTheory.Adjunction.Mates

Cited by

3 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category