Remark 88.13.5. 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 88.10.3. Thus Lemma 88.13.4 tells us

for predeformation functors. We will make the link with hulls in Remark 88.15.6.

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