## Tag `0CLL`

Chapter 86: Morphisms of Algebraic Stacks > Section 86.33: Valuative criteria

Lemma 86.33.11. The base change of a morphism of algebraic stacks which satisfies the existence part of the valuative criterion by any morphism of algebraic stacks is a morphism of algebraic stacks which satisfies the existence part of the valuative criterion.

Proof.Follows from Lemma 86.33.4 and the definition. $\square$

The code snippet corresponding to this tag is a part of the file `stacks-morphisms.tex` and is located in lines 7559–7565 (see updates for more information).

```
\begin{lemma}
\label{lemma-base-change-existence}
The base change of a morphism of algebraic stacks which satisfies the
existence part of the valuative criterion by any morphism of
algebraic stacks is a morphism of algebraic stacks which satisfies the
existence part of the valuative criterion.
\end{lemma}
\begin{proof}
Follows from Lemma \ref{lemma-cat-dotted-arrows-base-change}
and the definition.
\end{proof}
```

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