nLab ternary relation

A ternary relation (or triadic relation) is a relation in three variables (instead of the more common two of a binary relation).

The elementary theory of categories (in the strict sense) may be defined with a single ternary relation (and several axioms) in untyped predicate logic with equality; the relation holds of morphisms $f$, $g$, and $h$ if and only if $f$ is the composite (in a fixed order) of $g$ and $h$.