Theorems · Definition · category theory

CategoryTheory.ShortComplex.LeftHomologyMapData.map

{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] →
            {S₁ S₂ : CategoryTheory.ShortComplex C} →
              {φ : S₁ ⟶ S₂} →
                {h₁ : S₁.LeftHomologyData} →
                  {h₂ : S₂.LeftHomologyData} →
                    CategoryTheory.ShortComplex.LeftHomologyMapData φ h₁ h₂ →
                      (F : CategoryTheory.Functor C D) →
                        [inst_4 : F.PreservesZeroMorphisms] →
                          [inst_5 : h₁.IsPreservedBy F] →
                            [inst_6 : h₂.IsPreservedBy F] →
                              CategoryTheory.ShortComplex.LeftHomologyMapData (F.mapShortComplex.map φ) (h₁.map F)
                                (h₂.map F)

Given a left homology map data ψ : LeftHomologyMapData φ h₁ h₂ such that both left homology data h₁ and h₂ are preserved by a functor F, this is the induced left homology map data for the morphism F.mapShortComplex.map φ.

Defined in

Mathlib.Algebra.Homology.ShortComplex.PreservesHomology

Cited by

7 results in Mathlib

Foundations

Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Functor.PreservesZeroMorphismsCategoryTheory.ShortComplex.LeftHomologyData.IsPreservedByCategoryTheory.ShortComplex.LeftHomologyData.IsPreservedBy