Remark 90.7.6. Let $F: \mathcal{C}_\Lambda \to \textit{Sets}$ be a functor. Identifying functors with cofibered sets, the completion of $F$ is the functor $\widehat{F} : \widehat{\mathcal{C}}_\Lambda \to \textit{Sets}$ given by $\widehat{F}(S) = \mathop{\mathrm{lim}}\nolimits F(S/\mathfrak {m}_ S^{n})$. This agrees with the definition in Schlessinger's paper [Sch].

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