Departments of France Departments of France In the administrative divisions of France, the department (, ) is one of the three levels of government below the national level ("territorial collectivities"), between the administrative regions and the commune. Ninety-six departments are in metropolitan France, and five are overseas departments, which are also classified as regions. Departments are further subdivided into 334 arrondissements, themselves divided into cantons; the last two have no autonomy, and are used for the organisation of police, fire departments, and sometimes, elections. Each department is administered by an elected body called a departmental council ("conseil départemental" (sing.), "conseils départementaux" (plur.)). From
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