ofHomotopy — Mathlib

English

Given a homotopy ho between φ1 and φ2, the degree −1 cochain is defined by taking ho.hom as its values, i.e., ofHomotopy ho = Cochain.mk (p, q ↦ ho.hom p q).

Русский

При гомотопии ho между φ1 и φ2 коэффициент степени −1 задаётся значениями ho.hom: ofHomotopy ho = Cochain.mk (p, q ↦ ho.hom p q).

LaTeX

$$$$\mathrm{ofHomotopy}(\mathrm{ho}) = \mathrm{Cochain.mk}(p,q \mapsto \mathrm{ho.hom}(p,q)).$$$$

Lean4

/-- The cochain of degree `-1` given by an homotopy between two morphism of complexes. -/
def ofHomotopy {φ₁ φ₂ : F ⟶ G} (ho : Homotopy φ₁ φ₂) : Cochain F G (-1) :=
  Cochain.mk (fun p q _ => ho.hom p q)

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