alternatingConstHomotopyEquiv — Mathlib

English

Odd-case homology iso between alternatingConst and ShortComplex with φ, ψ and hOdd.

Русский

НеЧётный случай: изоморфия гомологии между alternatingConst и ShortComplex(φ, ψ, hOdd).

LaTeX

$$$\text{AltConstHomologyIsoOdd}(A, hOdd, hEven, hc).homology\, j \cong \mathrm{ShortComplex.mk}\; φ\; ψ\; hOdd$.homology$$

Lean4

/-- `alternatingConst.obj X` is homotopy equivalent to the chain
complex `(single₀ C).obj X`. -/
noncomputable def alternatingConstHomotopyEquiv (X : C) : HomotopyEquiv (alternatingConst.obj X) ((single₀ C).obj X) :=
  (HomotopyEquiv.ofIso (alternatingFaceMapComplexConst.app X).symm).trans
    ((SimplicialObject.Augmented.ExtraDegeneracy.const X).homotopyEquiv)

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