Lemma 65.7.3. Let $S$ be a scheme contained in $\mathit{Sch}_{fppf}$. Let $F \to H$, $G \to H$ be morphisms of algebraic spaces over $S$. Then $F \times _ H G$ is an algebraic space, and is a fibre product in the category of algebraic spaces over $S$.

**Proof.**
It follows from the stronger Lemma 65.7.2 that $F \times _ H G$ is an algebraic space. It is clear that $F \times _ H G$ is a fibre product in the category of algebraic spaces over $S$ since that is a full subcategory of the category of (pre)sheaves of sets on $(\mathit{Sch}/S)_{fppf}$.
$\square$

## 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Your email address will not be published.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)