Definition 90.19.2. Let $\mathcal{F}$ be a category cofibered in groupoids over $\mathcal C_\Lambda $. Let $x_0 \in \mathop{\mathrm{Ob}}\nolimits (\mathcal{F}(k))$. Assume a choice of pushforward $x_0 \to x_0'$ of $x_0$ along the map $k \to k[\epsilon ], a \mapsto a$ has been made. Then there is a unique map $x'_0 \to x_0$ such that $x_0 \to x_0' \to x_0$ is the identity on $x_0$. Then
\[ \text{Inf}_{x_0}(\mathcal F) = \text{Inf}(x'_0/x_0) \]
is the group of infinitesimal automorphisms of $x_0$
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