Probably a silly question. Suppose that $C$ is a category that does not have finite Cartesian products. So we cannot define a relation on some objects to be a sub object of their Cartesian product (a monic arrow into their Cartesian product). Is there some other natural notion that we can use $inside$ the category to generalise the notion of `relation'? I'm not interested in using the concretisation, so let's suppose $C$ is not concrete. 



Relations In Category Theory
You could describe a relation between $X$ and $Y$ to be a pair of maps $f\colon R\to X$, $g\colon R\to Y$, so that the family of maps $\{f,g\}$ is monic (meaning, if $fh=fh'$ and $gh=gh'$, then $h=h'$.)


