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.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

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.sup.i](G, F) (objects of Tab) for the continuous/topological group cohomology of G with coefficients in F.
Clearly, [??] is a functor from the category [??]-Filt of coherently filtered formal sheaves of modules to the category [??]-Filt of filtered formal sheaves of modules satisfying the functorial properties, moreover for any struct coherently filtered formal sheaf morphism [??] over [??] and for Y([[Florin].sub.1] [subset] Y([[Florin].sub.2] in [beta](Y), we get commutative diagrames of strict filtered morphisms.
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 &.
Their theory supplements the recent work of Asgari-Shahidi on the functorial life from (split and quasisplit forms of) GSpin2n to GL2n.
(10) (f, [f.sup.#]) : 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.
Nourani presents readers with comprehensive guide to new techniques with functorial models designed to address important areas of both pure mathematics and computability theory from the algebraic point of view.
This construction is functorial in the sense that a map f: X [right arrow] Y can also be rationalized to a map [f.sub.0]: [X.sub.0] [right arrow] [Y.sub.0] commuting with rationalisations.
For M [member of] [D.sup.b.sub.hol]([D.sub.X] there is a functorial isomorphism
We generalize this in Section 3, defining the functorial construction of a graded coalgebra Do C from graded coalgebras C and V.

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