leftHomologyIso_hom_naturality — Mathlib

English

There exists an isomorphism for leftRightHomologyComparison' when data h1,h2 are given and the system has homology.

Русский

Существует изоморфизм для leftRightHomologyComparison' при данных h1,h2 и наличии гомологии.

LaTeX

$$$\\text{isIso}(\\text{leftRightHomologyComparison}'(h_1,h_2))$$$

Lean4

@[reassoc]
theorem leftHomologyIso_hom_naturality :
    S₁.leftHomologyIso.hom ≫ homologyMap φ = leftHomologyMap φ ≫ S₂.leftHomologyIso.hom := by
  simpa only [LeftHomologyData.homologyIso_leftHomologyData, Iso.symm_inv] using
    LeftHomologyData.leftHomologyIso_inv_naturality φ S₁.leftHomologyData S₂.leftHomologyData

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