The Stacks project

Definition 90.21.4. Let $\mathcal{C}$ be a category. A groupoid in functors on $\mathcal{C}$ is representable if it is isomorphic to one of the form $(\underline{U}, \underline{R}, s, t, c)$ where $U$ and $R$ are objects of $\mathcal{C}$ and the pushout $R \amalg _{s, U, t} R$ exists.

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