# functor

(redirected from Functoriality)
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## functor

[′fəŋk·tər]
(computer science)
(mathematics)
A function between categories which associates objects with objects and morphisms with morphisms.

## functor

In category theory, a functor F is an operator on types. F is also considered to be a polymorphic operator on functions with the type

F : (a -> b) -> (F a -> F b).

Functors are a generalisation of the function "map". The type operator in this case takes a type T and returns type "list of T". The map function takes a function and applies it to each element of a list.
References in periodicals archive ?
We can then use Isomorphism Functoriality and parametricity of [expand.
Using the Isomorphism Functoriality Lemma and parametricity, we infer P[S [cross product] [N.
N*S using the Isomorphism Functoriality Lemma (Section 6) with the isomorphism S [equivalence] I [cross product] S.
This covariant functoriality was introduced by Content, Lemay and Leroux [9].
We then show that the two types of functoriality interact well enough that they can, in fact, be unified into a single functor.
We can now unify the two types of functoriality for incidence algebras.
Since each one of the present authors had an occasion to be frustrated with the search for a reference to a proof of the basic properties of the blow-up construction (especially properties having to do with functoriality in the smooth, or real analytic, category), we decided to write such a reference ourselves.
With this definition, the manifold structure of the blowup and especially its functoriality properties are not entirely obvious, and are somewhat awkward to prove.
It stresses naturality and functoriality and is coordinate-free as possible.
MATHEMATICAL EXPRESSION OMITTED] Functoriality then gives that

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