The Stacks project

Lemma 37.30.2. Let $f : X \to Y$ be a morphism of finite type. Let

\[ n_{X/Y} : Y \to \{ 0, 1, 2, 3, \ldots , \infty \} \]

be the function which associates to $y \in Y$ the dimension of $X_ y$. If $g : Y' \to Y$ is a morphism then

\[ n_{X'/Y'} = n_{X/Y} \circ g \]

where $X' \to Y'$ is the base change of $f$.

Proof. This follows from Morphisms, Lemma 29.28.3. $\square$

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