Theorems · Theorem · category theory

CategoryTheory.ShortComplex.mapOpcyclesIso_hom_naturality

∀ {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)
  (F : CategoryTheory.Functor C D) [inst_4 : F.PreservesZeroMorphisms] [inst_5 : S₁.HasRightHomology]
  [inst_6 : S₂.HasRightHomology] [inst_7 : F.PreservesRightHomologyOf S₁] [inst_8 : F.PreservesRightHomologyOf S₂],
  CategoryTheory.CategoryStruct.comp (CategoryTheory.ShortComplex.opcyclesMap (F.mapShortComplex.map φ))
      (S₂.mapOpcyclesIso F).hom =
    CategoryTheory.CategoryStruct.comp (S₁.mapOpcyclesIso F).hom (F.map (CategoryTheory.ShortComplex.opcyclesMap φ))

Defined in

Mathlib.Algebra.Homology.ShortComplex.PreservesHomology

Cited by

1 results in Mathlib

Foundations

Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Functor.PreservesZeroMorphismsCategoryTheory.ShortComplex.HasRightHomologyCategoryTheory.ShortComplex.HasRightHomologyCategoryTheory.Functor.PreservesRightHomologyOfCategoryTheory.Functor.PreservesRightHomologyOf