# The Stacks Project

## Tag 0CLP

Lemma 86.33.14. A closed immersion of algebraic stacks satisfies both the existence and uniqueness part of the valuative criterion.

Proof. Omitted. Hint: reduce to the case of a closed immersion of schemes by Lemmas 86.33.9 and 86.33.13. $\square$

The code snippet corresponding to this tag is a part of the file stacks-morphisms.tex and is located in lines 7720–7724 (see updates for more information).

\begin{lemma}
\label{lemma-closed-immersion-valuative-criteria}
A closed immersion of algebraic stacks satisfies both
the existence and uniqueness part of the valuative criterion.
\end{lemma}

\begin{proof}
Omitted. Hint: reduce to the case of a closed immersion of
schemes by Lemmas \ref{lemma-uniqueness-representable} and
\ref{lemma-existence-representable}.
\end{proof}

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