Theorems · Definition · category theory

CategoryTheory.LiftLeftAdjoint.constructLeftAdjoint

{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 B C} →
              {F : CategoryTheory.Functor C B} →
                (R : CategoryTheory.Functor A B) →
                  (F' : CategoryTheory.Functor C A) →
                    (adj₁ : F ⊣ U) →
                      (F' ⊣ R.comp U) →
                        [CategoryTheory.Limits.HasReflexiveCoequalizers A] →
                          ((X : B) → CategoryTheory.RegularEpi (adj₁.counit.app X)) → CategoryTheory.Functor B A

Construct the left adjoint to R, with object map constructLeftAdjointObj.

Defined in

Mathlib.CategoryTheory.Adjunction.Lifting.Left

Cited by

1 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasReflexiveCoequalizers