## Tag `0CLI`

Chapter 91: Morphisms of Algebraic Stacks > Section 91.38: Valuative criteria

Lemma 91.38.8. 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 91.38.5 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 8819–8825 (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}
```

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