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 ?
Filt of filtered formal sheaves of modules satisfying the functorial properties, moreover for any struct coherently filtered formal sheaf morphism [?
It is a sort of a dimension category, where the role of functorial maps is played by C-space transformations which reshuffles a p-brane history for a p'-brane history or a mixture of all of them, for example.
Since then, Chapoton [2] has given a functorial interpretation of this operation.
We generalize this in Section 3, defining the functorial construction of a graded coalgebra Do C from graded coalgebras C and V.