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