Theorems · Definition · category theory

CategoryTheory.LiftLeftAdjoint.constructLeftAdjointObj

{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) →
                    (F ⊣ U) → (F' ⊣ R.comp U) → [CategoryTheory.Limits.HasReflexiveCoequalizers A] → B → A

Construct the object part of the desired left adjoint as the coequalizer of F'Uε_Y with otherMap.

Defined in

Mathlib.CategoryTheory.Adjunction.Lifting.Left

Cited by

3 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasReflexiveCoequalizers