Theorems · Inductive type · category theory

CategoryTheory.Functor.IsLeftDerivedFunctor

{C : Type u_1} →
  {D : Type u_2} →
    {H : Type u_3} →
      [inst : CategoryTheory.Category.{v_1, u_1} C] →
        [inst_1 : CategoryTheory.Category.{v_3, u_2} D] →
          [inst_2 : CategoryTheory.Category.{v_5, u_3} H] →
            (LF : CategoryTheory.Functor D H) →
              {F : CategoryTheory.Functor C H} →
                {L : CategoryTheory.Functor C D} →
                  (L.comp LF ⟶ F) → (W : CategoryTheory.MorphismProperty C) → [L.IsLocalization W] → Prop

A functor LF : D ⥤ H is a left derived functor of F : C ⥤ H if it is equipped with a natural transformation α : L ⋙ LF ⟶ F which makes it a right Kan extension of F along L, where L : C ⥤ D is a localization functor for W : MorphismProperty C.

Defined in

Mathlib.CategoryTheory.Functor.Derived.LeftDerived

Cited by

33 results in Mathlib

Foundations

Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsLocalization