In Zermelo–Fraenkel set theory the collection of all sets is not a set; this follows from the axiom of foundation. One refers to collections that are not sets as proper classes. One cannot handle proper classes as one handles sets; in particular, one cannot write that those proper classes belong to a collection (either a set or a proper class). This is a problem because it means that the category of sets cannot be formalized straightforwardly in this setting. Categories like Set whose collection of objects forms a proper class are known as large categories, to distinguish them from the small categories whose objects form a set.