Definition 93.9.1. Let $S$ be a scheme contained in $\mathit{Sch}_{fppf}$. A $1$-morphism $f : \mathcal{X} \to \mathcal{Y}$ of categories fibred in groupoids over $(\mathit{Sch}/S)_{fppf}$ is called representable by algebraic spaces if for any $U \in \mathop{\mathrm{Ob}}\nolimits ((\mathit{Sch}/S)_{fppf})$ and any $y : (\mathit{Sch}/U)_{fppf} \to \mathcal{Y}$ the category fibred in groupoids

$(\mathit{Sch}/U)_{fppf} \times _{y, \mathcal{Y}} \mathcal{X}$

over $(\mathit{Sch}/U)_{fppf}$ is representable by an algebraic space over $U$.

There are also:

• 2 comment(s) on Section 93.9: Morphisms representable by algebraic spaces

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).