Is conormal sheaf a pullback?

Question

Apologize if this is a newbie question.

Let $i: Z\hookrightarrow X$ be a closed immersion with ideal sheaf $\mathscr{I}$. The conormal sheaf of $Z$ in $X$ is defined as $\mathscr{I}/\mathscr{I}^2$, regarded as a sheaf on $Z$.

Can the conormal sheaf be interpreted as $i^*\mathscr{I}$?

Answer 1

Yes, $$\mathscr I/\mathscr I^2=\mathscr I\otimes_{\mathcal O_X}\mathcal O_X/\mathscr I=i^*\mathscr I.$$ This is mentioned here.