Theorems · Definition · category theory

CategoryTheory.LiftRightAdjoint.constructRightAdjoint

{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) →
                      (L.comp F ⊣ U') →
                        [CategoryTheory.Limits.HasCoreflexiveEqualizers C] →
                          ((X : B) → CategoryTheory.RegularMono (adj₁.unit.app X)) → CategoryTheory.Functor B C

Construct the right adjoint to L, with object map constructRightAdjointObj.

Defined in

Mathlib.CategoryTheory.Adjunction.Lifting.Right

Cited by

1 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasCoreflexiveEqualizers