Just as a monoid consists of an underlying set with a binary operation on top of it which is closed, associative and with an identity, a category consists of an underlying digraph with an arrow composition operation on top of it which is transitively closed, associative, and with an identity at each object. In fact, a category's composition operation, when restricted to a single one of its objects, turns that object's set of arrows (which would all be loops) into a monoid.

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Monikers are often composed from other monikers to allow object hierarchies to be navigated based on a textual description of a path.