Definition 89.12.3. Let $\varphi : \mathcal{F} \to \mathcal{G}$ be a morphism predeformation categories. The differential $d \varphi : T \mathcal{F} \to T \mathcal{G}$ of $\varphi$ is the map obtained by evaluating the morphism of functors $\overline{\varphi }: \overline{\mathcal{F}} \to \overline{\mathcal{G}}$ at $A = k[\epsilon ]$.

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