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Given a universe $U$ and two subsets $S$ and $T$ (also, both members of $U$), what is the name given to denote the set of all binary relations in $U$ where the ordered pair $(S,T)$ is a member?

The concept I'm trying to describe is similar to $Hom(S,T)$ in a category of sets, but where as $Hom(S,T)$ is a category of all morphisms from $S$ to $T$, the concept I am targeting is: (1) limited in scope to sets; and (2) looking for all the morphisms for which $(S,T)$ are associated instead of for the morphisms from $S$ to $T$.

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