<sod>'''Category theory'''<ref>{{harnvb|Awodey|2006}}</ref> formalizes [[mathematical structure]] and its concepts in terms of a collection of structure-preserving [[maps]] or ''arrows'' (also called [[morphism]]s) over some defined collection. A [[Category (mathematics)|category]] has two basic properties: <eod>
<sod>'''Category theory'''<ref>{{harnvb|Awodey|2006}}</ref> formalizes [[mathematical structure]] and its concepts in terms of a collection of ''objects'' and of ''arrows'' (also called [[morphism]]s). A [[Category (mathematics)|category]] has two basic properties: the ability to [[Function composition|compose]] the arrows [[Associativity|associatively]] and the existence of an [[Identity function|identity]] arrow for each object. The language of Category theory has been used to formalize concepts of other high-level [[abstractions]] such as [[set theory|sets]], [[ring theory|rings]], and [[group theory|groups]].<eod>