Lemma 92.7.4. In Example 92.7.1 assume $P$ is a finitely generated graded $k$-algebra. Assume $\Lambda $ is a complete local ring with residue field $k$ (the classical case). Then the functor

of isomorphism classes of objects has a hull.

Lemma 92.7.4. In Example 92.7.1 assume $P$ is a finitely generated graded $k$-algebra. Assume $\Lambda $ is a complete local ring with residue field $k$ (the classical case). Then the functor

\[ F : \mathcal{C}_\Lambda \longrightarrow \textit{Sets},\quad A \longmapsto \mathop{\mathrm{Ob}}\nolimits (\mathcal{D}\! \mathit{ef}_ P(A))/\cong \]

of isomorphism classes of objects has a hull.

**Proof.**
This follows immediately from Lemmas 92.7.2 and 92.7.3 and Formal Deformation Theory, Lemma 89.16.6 and Remark 89.15.7.
$\square$

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