Theorems · Definition · category theory

CategoryTheory.NatTrans.leftDerivedToHomotopyCategory

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {D : Type u_1} →
      [inst_1 : CategoryTheory.Category.{v_1, u_1} D] →
        [inst_2 : CategoryTheory.Abelian C] →
          [inst_3 : CategoryTheory.HasProjectiveResolutions C] →
            [inst_4 : CategoryTheory.Abelian D] →
              {F G : CategoryTheory.Functor C D} →
                [inst_5 : F.Additive] →
                  [inst_6 : G.Additive] → (F ⟶ G) → (F.leftDerivedToHomotopyCategory ⟶ G.leftDerivedToHomotopyCategory)

The natural transformation F.leftDerivedToHomotopyCategory ⟶ G.leftDerivedToHomotopyCategory induced by a natural transformation F ⟶ G between additive functors.

Defined in

Mathlib.CategoryTheory.Abelian.LeftDerived

Cited by

5 results in Mathlib

Foundations

Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.HasProjectiveResolutionsCategoryTheory.AbelianCategoryTheory.Functor.AdditiveCategoryTheory.Functor.Additive