Lemma 10.149.3. Let $I \subset R$ be an ideal of a ring. The universal first order thickening of $R/I$ over $R$ is the surjection $R/I^2 \to R/I$. The conormal module of $R/I$ over $R$ is $C_{(R/I)/R} = I/I^2$.

**Proof.**
Omitted.
$\square$

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