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