If is a monoidal category, the unit -category is the -enriched category having one object, say , with , the monoidal unit object of , and the composition and identity-assigning morphisms being the canonical coherence isomorphism and the identity arrow , respectively.
The -category plays a role in enriched category theory that is similar to the role played by the terminal category in ordinary unenriched category theory. (In fact, the terminal category is the unit Set-category.) For instance, objects of a -category can be identified with -functors . Note that the unit -category is not a terminal object of , in general, just as is not usually terminal in .