Theorems · Definition · category theory

CategoryTheory.LiftRightAdjoint.otherMap

{A : Type u₁} →
  {B : Type u₂} →
    {C : Type u₃} →
      [inst : CategoryTheory.Category.{v₁, u₁} A] →
        [inst_1 : CategoryTheory.Category.{v₂, u₂} B] →
          [inst_2 : CategoryTheory.Category.{v₃, u₃} C] →
            {U : CategoryTheory.Functor A B} →
              {F : CategoryTheory.Functor B A} →
                (L : CategoryTheory.Functor C B) →
                  (U' : CategoryTheory.Functor A C) →
                    (F ⊣ U) → (L.comp F ⊣ U') → (X : B) → U'.obj (F.obj X) ⟶ U'.obj (F.obj (U.obj (F.obj X)))

(Implementation) To construct the right adjoint, we use the equalizer of U' F η_X with the composite U' F X ⟶ U' F L U' F X ⟶ U' F U F L U' F X ⟶ U' F U F X where the first morphism is ι_U'FX, the second is U' F η_LU'FX and the third is U' F U δ_FX. We will show that this equalizer exists and that it forms the object map for a right adjoint to L.

Defined in

Mathlib.CategoryTheory.Adjunction.Lifting.Right

Cited by

2 results in Mathlib

Foundations

Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category