On 15 Aug 2011, at 14:18, Bill Page wrote:
I know there are several people on this list interested in category theory and FriCAS/Axiom - including Ralf! ;) I don't think you should feel any concern that an argument that might or might not arise over terminology or even something more important. This is email and such arguments do not hurt (much) ... So if you have an opinion and/or some insight into this issue I would for one would be very happy to read it here. Start a new thread if it seems appropriate.
I would like to second this also. I have been wondering if it's possible to think about Axiom's type system using categorical language, and if the Axiom notion of a category can be aligned in some way with mathematical categories. I find myself getting confused when looking at the various functions and type constructors in the Axiom system, and I think to myself, can I hang all this complexity on some kind of broad categorical framework.
Such as, to a first approximation, functions between domains correspond to arrows between objects in some category, type constructors that take domains as arguments correspond to functors between categories, that sort of thing? Are there any articles/papers on this subject?
Maybe I'm way off-base here, but I'd like to hear how other people manage the complexity of the system in their heads.
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