Lemma 42.54.1. Let $(S, \delta )$ be as in Situation 42.7.1. Let

be a cartesian diagram of schemes locally of finite type over $S$ whose horizontal arrows are closed immersions. If $\mathcal{N}$ is a virtual normal sheaf for $Z$ in $X$, then $\mathcal{N}' = g^*\mathcal{N}$ is a virtual normal sheaf for $Z'$ in $X'$.

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