homologyMap_eq — Mathlib

English

For LeftHomologyData, homologyMap φ = h1.homologyIso.hom ≫ γ.φH ≫ h2.homologyIso.inv.

Русский

Для LeftHomologyData выполняется: homologyMap φ = h1.homologyIso.hom ≫ γ.φH ≫ h2.homologyIso.inv.

LaTeX

$$$\mathrm{homologyMap}(\varphi) = h_1.zhomo\;\mathrm{hom} \;\circ \gamma.\phi_H \circ h_2.homologyIso.inv$$$

Lean4

theorem homologyMap_eq : homologyMap φ = h₁.homologyIso.hom ≫ γ.φH ≫ h₂.homologyIso.inv :=
  by
  dsimp [homologyMap, LeftHomologyData.homologyIso, leftHomologyIso, LeftHomologyData.leftHomologyIso, homologyMap']
  simp only [← γ.leftHomologyMap'_eq, ← leftHomologyMap'_comp, id_comp, comp_id]

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