H1Iso — Mathlib

English

Induction principle analogue for H0: any property on H0 A follows from its values on images of A under H0π.

Русский

Аналогичный принцип индукции для H0: свойство на H0(A) следует из значений на образах A через H0π.

LaTeX

$$theorem H0_induction_on {C : H0 A → Prop} (x : H0 A) (h : ∀ x : A, C (H0π A x)) : C x$$

Lean4

/-- The 1st group homology of `A`, defined as the 1st homology of the complex of inhomogeneous
chains, is isomorphic to `cycles₁ A ⧸ boundaries₁ A`, which is a simpler type. -/
def H1Iso : H1 A ≅ (shortComplexH1 A).moduleCatLeftHomologyData.H :=
  (leftHomologyIso _).symm ≪≫ (leftHomologyMapIso' (isoShortComplexH1 A) _ _)

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