Theorems · Definition · category theory

CategoryTheory.LiftRightAdjoint.constructRightAdjointObj

{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') → [CategoryTheory.Limits.HasCoreflexiveEqualizers C] → B → C

Construct the object part of the desired right adjoint as the equalizer of U'Fη_Y with otherMap.

Defined in

Mathlib.CategoryTheory.Adjunction.Lifting.Right

Cited by

2 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasCoreflexiveEqualizers