The Stacks project

Remark 89.13.5. Let $F : \mathcal{C}_\Lambda \to \textit{Sets}$ be a predeformation functor satisfying (S1) and (S2). The condition $\dim _ k TF < \infty $ is precisely condition (H3) from Schlessinger's paper. Recall that (S1) and (S2) correspond to conditions (H1) and (H2), see Remark 89.10.3. Thus Lemma 89.13.4 tells us

\[ (H1) + (H2) + (H3) \Rightarrow \text{ there exists a versal formal object} \]

for predeformation functors. We will make the link with hulls in Remark 89.15.6.

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