# What are canonical injections for co-products in the category Rel?

What are canonical injections for co-products in the category Rel?

Coproducts in $\mathsf{Rel}$ look as follows: If $X,Y$ are objects, i.e. are just sets, then the underlying object of the coproduct is the disjoint union $X \sqcup Y$. This is equipped with maps of sets $X \to X \sqcup Y \leftarrow Y$. But every map of sets induces a relation (take its graph). These are the inclusion morphisms.