Theorems · Definition · category theory

ChainComplex.alternatingConstHomologyDataZero

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      (X : C) → (n : ℕ) → n = 0 → (HomologicalComplex.sc (ChainComplex.alternatingConst.obj X) n).HomologyData

The n-th homology of the alternating constant complex is X for n = 0.

Defined in: Mathlib.Algebra.Homology.AlternatingConst
Cited by: 0 results in Mathlib
Foundations: Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasZeroMorphisms

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Functor.objstatement and proof · cited by 19,642
CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
ComplexShape.downstatement · cited by 605
ChainComplexstatement · cited by 350
HomologicalComplex.scstatement and proof · cited by 205
CategoryTheory.ShortComplex.HomologyDatastatement · cited by 102
CategoryTheory.ShortComplex.HomologyData.ofZerosproof · cited by 10
ChainComplex.alternatingConststatement and proof · cited by 3

Cited by1

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ChainComplex.alternatingConstHomologyZeroproof · cited by 0