Theorems · Definition · category theory

CategoryTheory.ShortComplex.HomologyData.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] →
            {S : CategoryTheory.ShortComplex C} →
              (h : S.HomologyData) →
                (F : CategoryTheory.Functor C D) →
                  [inst_4 : F.PreservesZeroMorphisms] →
                    [h.left.IsPreservedBy F] → [h.right.IsPreservedBy F] → (S.map F).HomologyData

When a homology data h of a short complex S is such that both h.left and h.right are preserved by a functor F, this is the induced homology data h.map F for the short complex S.map F.

Defined in

Mathlib.Algebra.Homology.ShortComplex.PreservesHomology

Cited by

9 results in Mathlib

Foundations

Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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