Lemma 89.12.4. Let $\varphi : \mathcal{F} \to \mathcal{G}$ be a morphism of predeformation categories. Assume $\overline{\mathcal{F}}$ and $\overline{\mathcal{G}}$ both satisfy (S2). Then $d \varphi : T \mathcal{F} \to T \mathcal{G}$ is $k$-linear.

**Proof.**
In the proof of Lemma 89.12.2 we have seen that $\overline{\mathcal{F}}$ and $\overline{\mathcal{G}}$ satisfy the hypotheses of Lemma 89.11.8. Hence the lemma follows from Lemma 89.11.13.
$\square$

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## Comments (1)

Comment #1421 by Evan Warner on

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