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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.


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Their topics include quantum polynomials, isomorphisms and derivations of algebras, semigroup properties of cooperations on finite sets, continuous co-algebra endomorphisms of some complete ultra-metric Hopf algebras, irreducible sub-algebras of matrix Weyl algebras, the length of conjugacy classes and P-nilpotence of finite groups, a symbolic calculus on defect revisions of axiomatic systems, and conformal field theory and modular functor.
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.
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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