# 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 ?
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.
En tal medida, el alma, bajo la descripcion el Yo, es el functor que piensa y juzga.
Happen is represented as having the valency of an absolutive (or neutral) functor and a locative.
14] A functor maps isomorphic objects to isomorphic objects.
Let A and B be categories; then a functor from A to B is: a mapping F that sends objects of A to objects of B, and morphisms of A to morphisms of B in such a way that:
2] is an enriched functor in Cat that preserves the 2-category structure of [C.
Properties of direct image functor and inverse image functor are studied here in this paper, like coherence and exactness.
Un ideal de operadores entre espacios de Banach es un functor U que asocia a cada par de espacios de Banach E y F un subconjunto U(E, F) de L(E, F) tal que se cumplen las siguientes condiciones: para espacios de Banach arbitrarios E, F, G y H
The construction of this abelization is expressed in terms of category theory and as in the classical case of abelian groups it creates a functor called reflector.
Lanza stated that, in contrast to adult grammatical mixing which mainly includes mixing of content words, Siri seemed to mix functor words (defined as a closed class lexical items) more often than content words, a phenomenon that does not appear to be common according to what has been reported in most studies on bilingualism (although this phenomenon was also reported by Vihman; 1985).
Definition 7 Let C and D be categories, a functor F: C [right arrow] D is a pair of operations Fob: ObC [right arrow] ObD, Fmor:
Then (X,T) is finitistic if and only if (X, [chi] (T)) is [alpha]-finitistic where [chi] is the characteristic functor from Top to F-Top.

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