Theorems · Definition · category theory

CategoryTheory.ShortComplex.mapCyclesIso

{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 : CategoryTheory.Functor C D) →
                [inst_4 : F.PreservesZeroMorphisms] →
                  [inst_5 : S.HasLeftHomology] →
                    [inst_6 : F.PreservesLeftHomologyOf S] → (S.map F).cycles ≅ F.obj S.cycles

When a functor F preserves the left homology of a short complex S, this is the canonical isomorphism (S.map F).cycles ≅ F.obj S.cycles.

Defined in

Mathlib.Algebra.Homology.ShortComplex.PreservesHomology

Cited by

8 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.HasLeftHomologyCategoryTheory.Functor.PreservesLeftHomologyOf