Editing Category theory (section)

=== Further concepts and results ===
The definitions of categories and functors provide only the very basics of categorical algebra; additional important topics are listed below. Although there are strong interrelations between all of these topics, the given order can be considered as a guideline for further reading.
* The [[functor category]] ''D''<sup>''C''</sup> has as objects the functors from ''C'' to ''D'' and as morphisms the natural transformations of such functors. The [[Yoneda lemma]] is one of the most famous basic results of category theory; it describes representable functors in functor categories.
* [[Dual (category theory)|Duality]]: Every statement, theorem, or definition in category theory has a ''dual'' which is essentially obtained by "reversing all the arrows". If one statement is true in a category ''C'' then its dual is true in the dual category ''C''<sup>op</sup>. This duality, which is transparent at the level of category theory, is often obscured in applications and can lead to surprising relationships.
* [[Adjoint functors]]: A functor can be left (or right) adjoint to another functor that maps in the opposite direction. Such a pair of adjoint functors typically arises from a construction defined by a universal property; this can be seen as a more abstract and powerful view on universal properties.