We propose a set of operations for inquiring about the properties of individual objects and classes in an object-oriented database. The operations are closely related to the constructs introduced by our formalisation of the object-oriented data model, through which we unify the representation of the intensional and the extensional portions of the object-oriented database. As a consequence, they provide a uniform access to the extensional and the intensional parts of the object-oriented database. The proposed operations are used for inquiring about the associations among individual objects, the relationships between individual objects and class objects, and the relationships among the class objects themselves. We show that if they are integrated into an object algebra, they can serve for querying the intensional portion of the database, and for using the relationships between individual objects and the conceptual schema in conventional queries.