Theorems · Definition · category theory

CategoryTheory.Functor.mapHomologicalComplexCompIso

{ι : Type u_1} →
  {V : Type u} →
    [inst : CategoryTheory.Category.{v, u} V] →
      [inst_1 : CategoryTheory.Preadditive V] →
        {W : Type u_2} →
          [inst_2 : CategoryTheory.Category.{v_1, u_2} W] →
            [inst_3 : CategoryTheory.Preadditive W] →
              {W' : Type u_5} →
                [inst_4 : CategoryTheory.Category.{u_6, u_5} W'] →
                  [inst_5 : CategoryTheory.Preadditive W'] →
                    {F : CategoryTheory.Functor V W} →
                      {G : CategoryTheory.Functor W W'} →
                        {H : CategoryTheory.Functor V W'} →
                          (F.comp G ≅ H) →
                            [inst_6 : F.Additive] →
                              [inst_7 : G.Additive] →
                                [inst_8 : H.Additive] →
                                  (c : ComplexShape ι) →
                                    (F.mapHomologicalComplex c).comp (G.mapHomologicalComplex c) ≅
                                      H.mapHomologicalComplex c

If additive functors are related by an isomorphism F ⋙ G ≅ H, this is the corresponding isomorphism for the induced functors on categories of homological complexes.

Defined in

Mathlib.Algebra.Homology.Additive

Cited by

2 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Functor.AdditiveCategoryTheory.Functor.AdditiveCategoryTheory.Functor.Additive