Theorems · Theorem · category theory

HomologicalComplex.biprod_total_f

∀ {C : Type u_1} {ι : Type u_2} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preadditive C]
  {c : ComplexShape ι} (K L : HomologicalComplex C c)
  [inst_2 : ∀ (i : ι), CategoryTheory.Limits.HasBinaryBiproduct (K.X i) (L.X i)] (i : ι),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.biprod.fst.f i) (CategoryTheory.Limits.biprod.inl.f i) +
      CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.biprod.snd.f i) (CategoryTheory.Limits.biprod.inr.f i) =
    CategoryTheory.CategoryStruct.id ((K ⊞ L).X i)

Defined in: Mathlib.Algebra.Homology.HomologicalComplexBiprod
Cited by: 0 results in Mathlib
Foundations: Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Preadditive CategoryTheory.Limits.HasBinaryBiproduct

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CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement · cited by 32,603
CategoryTheory.CategoryStruct.compstatement · cited by 17,999
CategoryTheory.CategoryStruct.idstatement and proof · cited by 6,235
CategoryTheory.Preadditivestatement and proof · cited by 3,309
HomologicalComplex.Xstatement and proof · cited by 1,839
HomologicalComplexstatement and proof · cited by 1,691
ComplexShapestatement and proof · cited by 1,684
HomologicalComplex.Hom.fstatement and proof · cited by 845
CategoryTheory.Limits.biprodstatement and proof · cited by 312
CategoryTheory.Limits.HasBinaryBiproductstatement and proof · cited by 251
CategoryTheory.Limits.biprod.sndstatement · cited by 132

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