France is mainly divided into 18 administrative regions: 13 regions in metropolitan France (including the territorial collectivity of Corsica), and five located overseas. The regions are further subdivided into 101 departments, which are numbered mainly alphabetically. This number is used in postal codes and was formerly used on vehicle number plates. Among the 101 departments of France, five (French Guiana, Guadeloupe, Martinique, Mayotte, and Réunion) are in overseas regions (ROMs) that are also simultaneously overseas departments (DOMs), enjoy exactly the same status as metropolitan departments and are an integral part of the European Union. The 101 departments are subdivided into 335
Subdivided interval categories Subdivided interval categories In category theory (mathematics) there exists an important collection of categories denoted formula_1 for natural numbers formula_2. The objects of formula_3 are the integers formula_4, and the morphism set formula_5 for objects formula_6 is empty if formula_7. Subdivided interval categories are very useful in defining simplicial sets. The category whose objects are the subdivided interval categories and whose morphisms are functors is often written formula_8 and is called the simplicial indexing category. A simplicial set is just a contravariant functor formula_9. The category 𝟘 is an empty interval, that is, an empty category, having no objects nor