Remark 89.6.3. We say that a functor $F: \mathcal{C}_\Lambda \to \textit{Sets}$ is a *predeformation functor* if the associated cofibered set is a predeformation category, i.e. if $F(k)$ is a one element set. Thus if $\mathcal{F}$ is a predeformation category, then $\overline{\mathcal{F}}$ is a predeformation functor.

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