On Tue, Sep 16, 2008 at 3:21 AM, Ralf Hemmecke wrote:
>
>>> So "singleton" category can not be just one element set.
>>
>> ??? By *definition* it is a category that contains just one domain.
>> Are saying that this definition is inconsistent?
>
> Sounds like both of you don't understand each other.
>

Yes, perhaps that is true. I hope that by continuing this discussion
we can reach an agreement. Thanks for your attempt to help. :-)

> Let me use Aldor here...
>
> ---BEGIN aaa.as
> #include "aldor"
> C: Category == with;
> D: C == add;
> ---END aaa.as
>
> ---BEGIN bbb.as
> C: Category == with;
> D1: C == add;
> D2: C == add;
> ...
> Dn: C == add;
> ---END bbb.as
>
> In aaa.as C is a category that only has exactly one domain in it. But
> this is only true if I consider one fixed program.

C is not a "singleton" category. Something is not a singleton category
just because it happens to be used in one domain in some program.

> As bbb.as shows that "singleton" category definition depends on the
> context.

No, no, no. Currently there is no such thing as "singleton" category
in either Aldor or Spad so it is not possible to give an example of
it.

The singleton category 'Cat(D)' is *defined* as the category
containing just domain D. That is a definition - not something that
can be shown by an example.

> Thus, Waldek is right, that a category always contains (potentially)
> infinitely many domains (or in other words, one can define
> infinitely many domains to a given category).
>

Of course that is correct but it has nothing to do with what I meant
by singleton category.

> Did I understand you intentions correctly?

I am sorry, but no I do not think so. :-(

Ralf, did what I write about anonymous categories make sense to you?
I.e. that anonymous categories are not reflexive?

Regards,
Bill Page.

--~--~---------~--~----~------------~-------~--~----~
You received this message because you are subscribed to the Google Groups 
"FriCAS - computer algebra system" group.
To post to this group, send email to [email protected]
To unsubscribe from this group, send email to [EMAIL PROTECTED]
For more options, visit this group at 
http://groups.google.com/group/fricas-devel?hl=en
-~----------~----~----~----~------~----~------~--~---

Reply via email to