Manuscript XV-B@2 · XV-B.tex · proposition · 4d3f12e8

Proposition: Unrestricted corrections cancel algebraic defects

Reconstruction and the exact relative-lifting criterion › Unrestricted algebraic choices · lines 565–580 · proof included or linked

XV-B@2#prop:unrestricted

If a preliminary lift exists and $A = Hom (P_{int}, Y)$ , then $Ob_{A} (F_{0}) = 0$ .

Proof. Choose an algebraic complement $P_{int} = H \oplus L$ and its projection $π_{H} : P_{int} \to H$ . The correction

a = - d_{0} π_{H}

takes values in $Y$ and satisfies $a ∣_{H} = - d_{0}$ . Apply Theorem thm:lifting.

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