# functor

(redirected from Functorial)
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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 ?
An abelian group object F of BG is a sheaf on Top, together with actions yG(U) x F(U) [right arrow] F(U), functorial in U; we write [H.
Filt of filtered formal sheaves of modules satisfying the functorial properties, moreover for any struct coherently filtered formal sheaf morphism [?
El nuevo concepto de representacion, que bautizaremos como representacion homologica o functorial por motivos que se haran obvios mas adelante, es una generalizacion del concepto de representacion concebido como aplicacion (parcialmente) preservadora de estructura, tal como ha sido elucidado por diversos autores (por ejemplo, Mundy 1986, Swoyer 1989, Krantz et al.
in functional order) and the functorial action of &.
This construction is functorial in the sense that a map f: X [right arrow] Y can also be rationalized to a map [f.
Spec(B) [right arrow] Spec(A), yielding a functorial bijection
Since then, Chapoton [2] has given a functorial interpretation of this operation.
The protocol complex satisfies some useful functorial properties, which follow immediately from the definitions.
In order to retain crucial functorial properties of the construction that hold in the unital case, for instance: half exactness, one considers the unitization [(SM).
As far as they know, the Converse Theorem has not been used before to prove functorial transfer for a non-generic representative on a quasi-split group.
We generalize this in Section 3, defining the functorial construction of a graded coalgebra Do C from graded coalgebras C and V.
The functorial properties of E are easily verified, and it is evident that it commutes with [().

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