# The Stacks Project

## Tag 0CLG

Definition 91.38.6. Let $f : \mathcal{X} \to \mathcal{Y}$ be a morphism of algebraic stacks. We say $f$ satisfies the uniqueness part of the valuative criterion if for every diagram (91.38.1.1) and $\gamma$ as in Definition 91.38.1 the category of dotted arrows is either empty or a setoid with exactly one isomorphism class.

The code snippet corresponding to this tag is a part of the file stacks-morphisms.tex and is located in lines 8816–8824 (see updates for more information).

\begin{definition}
\label{definition-uniqueness}
Let $f : \mathcal{X} \to \mathcal{Y}$ be a morphism of algebraic stacks.
We say $f$ satisfies the {\it uniqueness part of the valuative criterion}
if for every diagram (\ref{equation-diagram}) and $\gamma$
as in Definition \ref{definition-fill-in-diagram}
the category of dotted arrows is either empty or
a setoid with exactly one isomorphism class.
\end{definition}

There are no comments yet for this tag.

There are also 2 comments on Section 91.38: Morphisms of Algebraic Stacks.

## Add a comment on tag 0CLG

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).