Remark 97.19.5. Let $f : \mathcal{X} \to \mathcal{Y}$ be a morphism of algebraic stacks. Let $x \in |\mathcal{X}|$ be a point. To indicate the equivalent conditions of Lemma 97.19.4 are satisfied for $f$ and $x$ in the literature the terminology *$f$ is stabilizer preserving at $x$* or *$f$ is fixed-point reflecting at $x$* is used. We prefer to say *$f$ induces an isomorphism between automorphism groups at $x$ and $f(x)$*.

## Post a comment

Your email address will not be published.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 toolbar).

Unfortunately JavaScript is disabled in your browser, so the comment preview function will not work.

All contributions are licensed under the GNU Free Documentation License.

## Comments (0)

There are also: