Inductive limits of projective C*-algebras. - IMAR
Inductive limits of projective C*-algebras. - IMAR
Inductive limits of projective C*-algebras. - IMAR
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Relations between the different classes I<br />
Lemma 4.1<br />
Given α: A → P, β: P → A with β ◦α = id A and P <strong>projective</strong>.<br />
⇒ A <strong>projective</strong>.<br />
Pro<strong>of</strong>.<br />
Given lifting problem ϕ: A → C/J, need lift ψ : A → C.<br />
A α<br />
P<br />
id A<br />
β<br />
ω<br />
A<br />
C<br />
π<br />
ϕ C/J<br />
P <strong>projective</strong> ⇒ get lift ω: P → C for ϕ◦β: P → C/J<br />
Then ψ := ω ◦α : A → B is desired lift for ϕ<br />
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