# The Stacks Project

## Tag 0CLM

Lemma 86.33.12. The composition of morphisms of algebraic stacks which satisfy the existence part of the valuative criterion is another morphism of algebraic stacks which satisfies the existence part of the valuative criterion.

Proof. Follows from Lemma 86.33.5 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 7572–7578 (see updates for more information).

\begin{lemma}
\label{lemma-composition-existence}
The composition of morphisms of algebraic stacks which satisfy the
existence part of the valuative criterion is another
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-composition}
and the definition.
\end{proof}

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