The Stacks project

Definition 90.12.3. 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 $A = k[\epsilon ]$.