Theorems · Definition · category theory

CategoryTheory.ShortComplex.HomologyMapData.natTransApp

{C : Type u_1} →
  {D : Type u_2} →
    [inst : CategoryTheory.Category.{v_1, u_1} C] →
      [inst_1 : CategoryTheory.Category.{v_2, u_2} D] →
        [inst_2 : CategoryTheory.Limits.HasZeroMorphisms C] →
          [inst_3 : CategoryTheory.Limits.HasZeroMorphisms D] →
            {S : CategoryTheory.ShortComplex C} →
              {F G : CategoryTheory.Functor C D} →
                [inst_4 : F.PreservesZeroMorphisms] →
                  [inst_5 : G.PreservesZeroMorphisms] →
                    [inst_6 : F.PreservesLeftHomologyOf S] →
                      [inst_7 : G.PreservesLeftHomologyOf S] →
                        [inst_8 : F.PreservesRightHomologyOf S] →
                          [inst_9 : G.PreservesRightHomologyOf S] →
                            (h : S.HomologyData) →
                              (τ : F ⟶ G) →
                                CategoryTheory.ShortComplex.HomologyMapData (S.mapNatTrans τ) (h.map F) (h.map G)

Given a natural transformation τ : F ⟶ G between functors C ⥤ D which preserve the homology of a short complex S, and a homology data for S, this is the homology map data for the morphism S.mapNatTrans τ obtained by evaluating τ.

Defined in

Mathlib.Algebra.Homology.ShortComplex.PreservesHomology

Cited by

2 results in Mathlib

Foundations

Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Functor.PreservesZeroMorphismsCategoryTheory.Functor.PreservesZeroMorphismsCategoryTheory.Functor.PreservesLeftHomologyOfCategoryTheory.Functor.PreservesLeftHomologyOfCategoryTheory.Functor.PreservesRightHomologyOfCategoryTheory.Functor.PreservesRightHomologyOf