The Stacks project

Lemma 29.29.3. Let $f : X \to Y$, $g : Y \to Z$ be locally of finite type. If $f$ has relative dimension $\leq d$ and $g$ has relative dimension $\leq e$ then $g \circ f$ has relative dimension $\leq d + e$. If

  1. $f$ has relative dimension $d$,

  2. $g$ has relative dimension $e$, and

  3. $f$ is flat,

then $g \circ f$ has relative dimension $d + e$.

Proof. This is immediate from Lemma 29.28.2. $\square$

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