Theorems · Theorem · category theory

HomologicalComplex.cyclesMap_comp_assoc

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  {ι : Type u_2} {c : ComplexShape ι} {K L M : HomologicalComplex C c} (φ : K ⟶ L) (ψ : L ⟶ M) (i : ι)
  [inst_2 : K.HasHomology i] [inst_3 : L.HasHomology i] [inst_4 : M.HasHomology i] {Z : C} (h : M.cycles i ⟶ Z),
  CategoryTheory.CategoryStruct.comp (HomologicalComplex.cyclesMap (CategoryTheory.CategoryStruct.comp φ ψ) i) h =
    CategoryTheory.CategoryStruct.comp (HomologicalComplex.cyclesMap φ i)
      (CategoryTheory.CategoryStruct.comp (HomologicalComplex.cyclesMap ψ i) h)

Defined in: Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex
Cited by: 0 results in Mathlib
Foundations: Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasZeroMorphisms HomologicalComplex.HasHomology HomologicalComplex.HasHomology HomologicalComplex.HasHomology

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CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
CategoryTheory.Category.assocproof · cited by 6,433
CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
HomologicalComplexstatement and proof · cited by 1,691
ComplexShapestatement and proof · cited by 1,684
HomologicalComplex.HasHomologystatement and proof · cited by 342
HomologicalComplex.cyclesstatement and proof · cited by 164
HomologicalComplex.cyclesMapstatement and proof · cited by 59
HomologicalComplex.cyclesMap_compproof · cited by 3

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