The following conditions are equivalent:
-
1.
The relation $R$ is a retraction in $\mathsf{Rel}$.
-
2.
We have $R=\operatorname {\mathrm{Gr}}(f)$ for some injective function $f\colon A\to B$.
8.5.12 Retractions
Let $R\colon A\mathrel {\rightarrow \kern -9.5pt\mathrlap {|}\kern 6pt}B$ be a relation.
Proof of Proposition 8.5.12.1.1.
Omitted.
