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 ff, gg, and hh if and only if ff is the composite (in a fixed order) of gg and hh.

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