The Stacks project

\begin{equation} \label{groupoids-quotients-equation-list} \begin{matrix} j_{diag} & : & U & \longrightarrow & U \times _ B U, & u & \longmapsto & (u, u) \\ j_{flip} & : & R & \longrightarrow & U \times _ B U, & r & \longmapsto & (s(r), t(r)) \\ j_{comp} & : & R \times _{s, U, t} R & \longrightarrow & U \times _ B U, & (r, r') & \longmapsto & (t(r), s(r')) \end{matrix} \end{equation}