Editing Functor (section)

== Relation to other categorical concepts ==
Let ''C'' and ''D'' be categories. The collection of all functors from ''C'' to ''D'' forms the objects of a category: the [[functor category]]. Morphisms in this category are [[natural transformation]]s between functors.

Functors are often defined by [[universal property|universal properties]]; examples are the [[tensor product]], the [[direct sum of modules|direct sum]] and [[direct product]] of groups or vector spaces, construction of free groups and modules, [[direct limit|direct]] and [[inverse limit|inverse]] limits. The concepts of [[limit (category theory)|limit and colimit]] generalize several of the above.

Universal constructions often give rise to pairs of [[adjoint functors]].