nLab
representable morphism of stacks

A morphism $f:X\to Y$ of stacks over a site $C$ is called representable if for all representable objects $U\in C\stackrel{Y}{\hookrightarrow }\mathrm{Stacks}(C)$ and all morphisms $U\to Y$ the homotopy pullback $X{\times }_{Y}U$ in

$$\begin{array}{ccc}X{\times }_{Y}U& \to & X\\ \downarrow & {}^{\simeq }⇙& {\downarrow }^f\\ U& \to & Y\end{array}$$\array{ X \times_Y U &\to& X \\ \downarrow &{}^{\simeq}\swArrow& \downarrow^f \\ U &\to& Y }

is again representable.