Difference between revisions of "Functor"
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| − | In [[category theory]], a '''functor''' is a | + | In [[category theory]], a '''functor''' is a type of function between categories. Functors can be thought of as [[morphism]]s in the category of small categories. |
Functors were first proposed in [[algebraic topology]], where algebraic objects such as the [[fundamental group]] are associated to [[topological space]]s, and algebraic [[homomorphism]]s are associated to continuous functions. Recently, functors are used to relate various categories. | Functors were first proposed in [[algebraic topology]], where algebraic objects such as the [[fundamental group]] are associated to [[topological space]]s, and algebraic [[homomorphism]]s are associated to continuous functions. Recently, functors are used to relate various categories. | ||
Revision as of 21:31, March 14, 2007
In category theory, a functor is a type of function between categories. Functors can be thought of as morphisms in the category of small categories.
Functors were first proposed in algebraic topology, where algebraic objects such as the fundamental group are associated to topological spaces, and algebraic homomorphisms are associated to continuous functions. Recently, functors are used to relate various categories.