RE: [Axiom-developer] Complex exponentiation and 0

[Bertfried Fauser]

On Mon, 21 Jun 2004, Page, Bill wrote:

> I am inclined to reject this argument on the general grounds of
> the current treatment of categories with initial objects.
>
> In the category of cardinal numbers a "map" is a morphism and 0
> is initial. I think card.spad should be understood as implementing
> such a category, although strictly speaking of course Axiom does
> not (yet?) fully conform to category theory in this respect.

I agree totally with this. However, there are categories which have more
subtle structure being able to cope with notions as smoothnes etc. Such
categories bahave different. It is usually easily possible to write down
"elements" (not belonging to the category but looking formally like them)
which behave different. Eg if x^y is smooth in x and y there is no
problem. I do however not know how AXIOM could learn to be fully
categorial in this sense.

ciao
BF.

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