cocyclesIso₀_inv_comp_iCocycles

English

The inverse of cocyclesIso0 composed with iCocycles equals shortComplexH0 f composed with cochainsIso0 inverse.

Русский

Обратное cocyclesIso0, затем iCocycles, равно короткому комплексу H0, умноженному на обратное коцепи0.

LaTeX

$$$(cocyclesIso_0(A)).inv \\circ iCocycles(A,0) = (shortComplexH0(A)).f \\circ (cochainsIso_0(A)).inv$$

Lean4

@[reassoc (attr := simp), elementwise (attr := simp)]
theorem cocyclesIso₀_inv_comp_iCocycles :
    (cocyclesIso₀ A).inv ≫ iCocycles A 0 = (shortComplexH0 A).f ≫ (cochainsIso₀ A).inv := by
  rw [Iso.inv_comp_eq, ← Category.assoc, Iso.eq_comp_inv, cocyclesIso₀_hom_comp_f]

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