Theorems · Definition · category theory

CategoryTheory.Functor.leftDerivedNatTrans

{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' LF : CategoryTheory.Functor D H) →
              {F F' : CategoryTheory.Functor C H} →
                {L : CategoryTheory.Functor C D} →
                  (L.comp LF' ⟶ F') →
                    (α : L.comp LF ⟶ F) →
                      (W : CategoryTheory.MorphismProperty C) →
                        [inst_3 : L.IsLocalization W] → [LF.IsLeftDerivedFunctor α W] → (F' ⟶ F) → (LF' ⟶ LF)

The natural transformation LF' ⟶ LF on left derived functors that is induced by a natural transformation F' ⟶ F.

Defined in

Mathlib.CategoryTheory.Functor.Derived.LeftDerived

Cited by

10 results in Mathlib

Foundations

Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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