nLab name of the relation

Definition

Take a topos $\mathcal{E}$ and a monic $\rho \colon R \hookrightarrow B \times A$ (thought of as a relation between $A$ and $B$). The name of $R$ is then the transpose $r \colon B \rightarrow \Omega^A$ of the characteristic map $\phi_{\rho} \colon B \times A \rightarrow \Omega$ of $\rho$ in $\mathcal{E}$.

References

Peter Johnstone, Sketches of an Elephant Section A2.1