shortComplexH0_exact — Mathlib

English

The 0-cocycles of inhomogeneous cochains are isomorphic to A.ρ.invariants.

Русский

0-коциклы инhomogeneous cochains изоморфны инвариантам A.ρ.

LaTeX

$$cocycles_0(A) \\cong ModuleCat.of k (A.\\rho.invariants)$$

Lean4

theorem shortComplexH0_exact : (shortComplexH0 A).Exact :=
  by
  rw [ShortComplex.moduleCat_exact_iff]
  intro (x : A) (hx : d₀₁ _ x = 0)
  refine ⟨⟨x, fun g => ?_⟩, rfl⟩
  rw [← sub_eq_zero]
  exact congr_fun hx g

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