## Tag `0CLI`

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

Lemma 87.38.8. The composition of morphisms of algebraic stacks which satisfy the uniqueness part of the valuative criterion is another morphism of algebraic stacks which satisfies the uniqueness part of the valuative criterion.

Proof.Follows from Lemma 87.38.5 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 8775–8781 (see updates for more information).

```
\begin{lemma}
\label{lemma-composition-uniqueness}
The composition of morphisms of algebraic stacks which satisfy the
uniqueness part of the valuative criterion is another
morphism of algebraic stacks which satisfies the
uniqueness part of the valuative criterion.
\end{lemma}
\begin{proof}
Follows from Lemma \ref{lemma-cat-dotted-arrows-composition}
and the definition.
\end{proof}
```

## Comments (0)

## Add a comment on tag `0CLI`

Your email address will not be published.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.