Theorems · Definition · category theory

HomologicalComplex.biprodXIso

{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) → (K ⊞ L).X i ≅ K.X i ⊞ L.X i

The canonical isomorphism (K ⊞ L).X i ≅ (K.X i) ⊞ (L.X i).

Defined in

Mathlib.Algebra.Homology.HomologicalComplexBiprod

Cited by

9 results in Mathlib

Foundations

Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Limits.HasBinaryBiproduct