Classification Theorem

A classification theorem answers the classification problem, which asks what the objects of a given type are, up to some equivalence. The cited article explains that it gives a non-redundant enumeration in which each object is equivalent to exactly one class. It connects the idea to related problems: the equivalence problem asks whether two given objects are equivalent, a complete set of invariants together with which invariants are realizable solves the classification problem, and a canonical form solves the classification problem while carrying more data. Theorems that sort a family of mathematical objects into complete lists of types are grouped under this concept.