The Stacks project

Remark 90.21.6. We will say “let $(\underline{U}, \underline{R}, s, t, c)$ be a groupoid in functors on $\mathcal{C}$” to mean that we have a representable groupoid in functors. Thus this means that $U$ and $R$ are objects of $\mathcal{C}$, there are morphisms $s, t : U \to R$, the pushout $R \amalg _{s, U, t} R$ exists, there is a morphism $c : R \to R \amalg _{s, U, t} R$, and $(\underline{U}, \underline{R}, s, t, c)$ is a groupoid in functors on $\mathcal{C}$.