Theorems · Definition · category theory

CategoryTheory.LiftRightAdjoint.constructRightAdjointEquiv

{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) →
                    (adj₁ : F ⊣ U) →
                      (adj₂ : L.comp F ⊣ U') →
                        [inst_3 : CategoryTheory.Limits.HasCoreflexiveEqualizers C] →
                          ((X : B) → CategoryTheory.RegularMono (adj₁.unit.app X)) →
                            (Y : C) →
                              (X : B) →
                                (Y ⟶ CategoryTheory.LiftRightAdjoint.constructRightAdjointObj L U' adj₁ adj₂ X) ≃
                                  (L.obj Y ⟶ X)

The homset equivalence which helps show that L is a left adjoint.

Defined in

Mathlib.CategoryTheory.Adjunction.Lifting.Right

Cited by

3 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasCoreflexiveEqualizers