English
There is a canonical isomorphism between X(K.op i) and Opposite.op(X(K i)) for each index i.
Русский
Канада каноническое изоморфизм между X(K.op i) и Opposite.op(X(K i)).
LaTeX
$$XOpIso : ∀ i, X K.op i ≅ Opposite.op (X K i)$$
Lean4
/-- Given `h : ConnectData K L` and `n : ℕ`, the homology
of `h.cochainComplex` in degree `-(n + 2)` identifies to the homology of `K` in degree `n + 1`. -/
noncomputable def homologyIsoNeg (n : ℕ) (m : ℤ) [h.cochainComplex.HasHomology m] [K.HasHomology (n + 1)]
(hm : m = -(n + 2 : ℕ)) : h.cochainComplex.homology m ≅ K.homology (n + 1) :=
have := hasHomology_of_iso h.restrictionLEIso.symm (n + 1)
(h.cochainComplex.restrictionHomologyIso (ComplexShape.embeddingUpIntLE (-1)) (n + 2) (n + 1) n (by simp) (by simp)
(i' := m - 1) (j' := m) (k' := m + 1) (by simp; cutsat) (by simp; cutsat) (by simp; cutsat) (by simp)
(by simp)).symm ≪≫
HomologicalComplex.homologyMapIso h.restrictionLEIso (n + 1)
