Theorems · Definition · category theory

CategoryTheory.ShortComplex.HomologyMapData.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.HomologyData} →
                  {h₂ : S₂.HomologyData} →
                    CategoryTheory.ShortComplex.HomologyMapData φ h₁ h₂ →
                      (F : CategoryTheory.Functor C D) →
                        [inst_4 : F.PreservesZeroMorphisms] →
                          [inst_5 : h₁.left.IsPreservedBy F] →
                            [inst_6 : h₁.right.IsPreservedBy F] →
                              [inst_7 : h₂.left.IsPreservedBy F] →
                                [inst_8 : h₂.right.IsPreservedBy F] →
                                  CategoryTheory.ShortComplex.HomologyMapData (F.mapShortComplex.map φ) (h₁.map F)
                                    (h₂.map F)

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

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.ShortComplex.LeftHomologyData.IsPreservedByCategoryTheory.ShortComplex.RightHomologyData.IsPreservedByCategoryTheory.ShortComplex.LeftHomologyData.IsPreservedByCategoryTheory.ShortComplex.RightHomologyData.IsPreservedBy