Bill Page wrote:
>
> On 20 October 2016 at 06:16, oldk1331 <[email protected]> wrote:
> > About abstracting the signature 'map : (S->S,%)->%'
> > into a category, there are 2 problems so far:
> >
> >> - Functor is quite loaded name and may lead to confusion.
> >> Something like 'MapCategory2' seem to fit better existing
> >> naming scheme.
> >> - What documentatin do you propose for the 'map' function?
> >> Current scheme with several signatures has a separate
> >> documentation slot per signature. Common signature would
> >> be quite abstract, so hard to specify.
> >
> > First, the name. Yes, the name "Functor" may lead to
> > confusion, for example, to be mixed with the category
> > theory "Functor". (Well, "Category" has similar problem.)
> > OpenAxiom uses "Functorial", which is similar to "Functor"?
> > I think we can also consider the name "MapCategory".
>
> I am against category names that include the word Category in the
> name. 'SetCategory' is already annoying enough. I think the name
> should reflect the terminology used in the (preferably widely
> accepted) mathematical literature for the relevant concept.
Well, I agree that we should follow mathematical literature
if possible. However, mathematical terminology is frequently
overloaded and in case of types we need to do some renaming
to disabiguate. And we have cases where we have categories
of objects which behave like some mathematical concept
and a distingushed domain of such category. Current convention
for such cases is Foo for domain and FooCategory for category.
AFAICS there are tens of categories using word Category in
the name and there are good reasons to have more of them.
Concerning Functor: principal use is in category theory,
where is means morphism (mapping) between categories.
Clearly the proposed thing is not a functor in such
sense. The word Functor is used in Spad compiler
and using it with other meaning will create confusion.
And while using a different terminology is Spad
compiler is possible the proposed use of Functor
diverges from mathematical practice at least as much
as current use in Spad compiler.
--
Waldek Hebisch
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