Theorems · Definition · category theory

CategoryTheory.Functor.isPointwiseRightKanExtensionOfHasPointwiseLeftDerivedFunctor

{C : Type u₁} →
  {D : Type u₂} →
    {H : Type u₃} →
      [inst : CategoryTheory.Category.{v₁, u₁} C] →
        [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
          [inst_2 : CategoryTheory.Category.{v₃, u₃} H] →
            (F' : CategoryTheory.Functor D H) →
              {F : CategoryTheory.Functor C H} →
                {L : CategoryTheory.Functor C D} →
                  (α : L.comp F' ⟶ F) →
                    (W : CategoryTheory.MorphismProperty C) →
                      [F.HasPointwiseLeftDerivedFunctor W] →
                        [inst_4 : L.IsLocalization W] →
                          [F'.IsLeftDerivedFunctor α W] →
                            (CategoryTheory.Functor.RightExtension.mk F' α).IsPointwiseRightKanExtension

A left derived functor is a pointwise left derived functor when there exists a pointwise left derived functor.

Defined in

Mathlib.CategoryTheory.Functor.Derived.PointwiseLeftDerived

Cited by

0 results in Mathlib

Foundations

Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.HasPointwiseLeftDerivedFunctorCategoryTheory.Functor.IsLocalizationCategoryTheory.Functor.IsLeftDerivedFunctor