Editing Category (mathematics) (section)

==Small and large categories==

A category ''C'' is called '''small''' if both ob(''C'') and mor(''C'') are actually [[Set (mathematics)|sets]] and not [[proper class]]es, and '''large''' otherwise. A '''locally small category''' is a category such that for all objects ''a'' and ''b'', the hom-class hom(''a'', ''b'') is a set, called a '''homset'''. Many important categories in mathematics (such as the category of sets), although not small, are at least locally small.  Since, in small categories, the objects form a set, a small category can be viewed as an [[algebraic structure]] similar to a [[monoid]] but without requiring [[closure (mathematics)|closure]] properties.  Large categories on the other hand can be used to create "structures" of algebraic structures.