> 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.
OK, but then you should more rigorously explain how "Cat" fits in a
non-contratictory way into the Aldor/SPAD language. (Sounds like you are
thinking of yet another language... which was not clear to me up to now).
> Ralf, did what I write about anonymous categories make sense to you?
> I.e. that anonymous categories are not reflexive?
Ehm, you mean whether the category
with
equals the category
with
or rather is not equal. I think we have discussed that before, but now
we have 3 mailing archives to look for such a thread. :-( But maybe it
is on aldor-l.
The point is, I would not bet. In
D1: with == add ...
D2: with == add ...
the "with" appears in "type context" (see AUG). Now, whether that has
something to do with "reflexiveness", I don't know. But, I would see
"with" rather as a function than a constant. So, being in type context,
you cannot know whether the two "with"s are equal or not.
In this case also "has" does not help you to decide whether these
"with"s are equal or not, since
(D1 has with) and (D2 has with)
will certainly return true.
Does that help?
Ralf
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