# functor

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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 ?
A categorical modeling is to construct categories for which it is possible to find functors allowing the construction of categories that model a MAS.
If G : A [right arrow] B is a functor such that every G-structured source has a G-initial lift, then the following conditions are equivalent:
Conversely given a groupoid g and a group G with a star injective functor F : Q [right arrow]* G (viewing G as a small category with one object), we can associate a partial action of G on the set of objects X = [Q.sup.(0]).
Application of the functor [[GAMMA].sub.xR](-) to the monomorphism [mathematical expression not reproducible] yields a monomorphism [mathematical expression not reproducible].
Hence [G.sub.2]: NSet(H) [right arrow] ISet(H) is a functor.
Por lo mismo, entre todos los factores funcionales de la subjetividad que piensa, juzga y conoce analizados por Kant, el Yo que piensa y opera constituye, dicho en el lenguaje de la teoria sintactica moderna, el functor no linguistico supremo (68).
Hence, ' is a contravariant functor that is obviously period two.
(1) The interlayer operations inherit the mixture of intra- and interlayer operations and (2) there is a procedure by which the interlayer operation can be regarded as an adjoint functor. If the interlayer operation satisfies the conditions (1) and (2), it is called a prefunctor [55].
Definition 2 A species (with restrictions) is a contravariant functor P: [set.sup.x] [right arrow] Set from the category of finite sets with injections to the category of all sets.
In contrast with previous works, the current study is based on phonological and functor innovations.
From Theorems 27 and 28 it follows that the procedure assigning to each soft fuzzy proximity [delta] generated soft fuzzy topology [[tau].sub.[delta]] and leaving morphisms unchanged can be interpreted as a functor.
Finally we observe that, from the continuity of the Cech cohomology functor, we can say that any [R.sub.[delta]] set is also an acyclic space.

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