nLab
name of the relation

Definition

Take a topos $ℰ$ and a monic $\rho :R\hookrightarrow B\times A$ (thought of as a relation between $A$ and $B$). The name of $R$ is then the transpose $r:B\to A$ of the characteristic map ${\varphi }_{\rho }:B\times A\to \Omega$ of $\rho$ in $ℰ$.

References

Peter Johnstone, Sketches of an Elephant Section A2.1