## Tag `0CLL`

Chapter 87: Morphisms of Algebraic Stacks > Section 87.38: Valuative criteria

Lemma 87.38.11. 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 87.38.4 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 8863–8869 (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}
```

## Comments (0)

## Add a comment on tag `0CLL`

Your email address will not be published. Required fields are marked.

In your comment you can use Markdown and LaTeX style mathematics (enclose it like `$\pi$`

). A preview option is available if you wish to see how it works out (just click on the eye in the lower-right corner).

All contributions are licensed under the GNU Free Documentation License.

There are no comments yet for this tag.

There are also 2 comments on Section 87.38: Morphisms of Algebraic Stacks.