Why is the (GoF) Flyweight a structural (and not a creational) design pattern?

The essence of the Flyweight pattern is not creation of objects but sharing of them. The pattern states that the objects to be shared are usually held in some external data structure but does not specify how those data structures are created or represented.

What makes the pattern structural is the use of factory-like class to obtain the flyweights. This imposes a static structure on the design.