Theorems · Definition · category theory

CategoryTheory.Functor.rightDerivedNatTrans

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

The natural transformation RF ⟶ RF' on right derived functors that is induced by a natural transformation F ⟶ F'.

Defined in

Mathlib.CategoryTheory.Functor.Derived.RightDerived

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.IsRightDerivedFunctor