The Stacks project

Remark 90.13.5. 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 90.10.3. Thus Lemma 90.13.4 tells us

for predeformation functors. We will make the link with hulls in Remark 90.15.6.