Dear Martin, I may have some of the same concerns as Ralf. Some time ago I read some slides, (which Bill pointed me to? but I forgot where to find them) about using category theory in/for computer algebra (it may be still on the axiom webpage somewhere). So there have been people already thinking about this....
>> 1) I don't quite understand the benefit of this domain other than >> perhaps drawing diagrams. What is your actual motivation for such a domain. With homsets, you define arrows in a small concrete category, not every category is representable. Also, this is just another way of defining a `set' of arrows, so your function first point of view is not pure here. Computation with states may be modelled within a framework of (categorical) coalgebras. To do so you need the concept of a functor. Just homsets will not do. Maclane said that category theory was invented just to be able to talk about functors and natural transformations. It would hence be really necessary to be able to iterate your constructions, having `homsets' on a category (note that is not just homsets on homsets). Another thing which comes into my mind are such constructions as equalizers and coequalizers, and properties of arrows such as monic, epic, which are necessary to infere the commutativity of pull-back or push-out diagrams. So arrows come with atributes. Categories can be defined using graphs, see for example Lambek - Scott, introduction to higher order categorical logic. But to make them versatile needs much more. >From a computational point of view, I would like to have categorical structures in AXIOM such as monads. (As Haskel has). These are really power full tools to write very abstract fancy programs. Anyhow, if you can cook up something useful, anybody will be happy. Cheers BF. -- % PD Dr Bertfried Fauser % Research Fellow, School of Computer Science, Univ. of Birmingham % Honorary Associate, University of Tasmania % Privat Docent: University of Konstanz, Physics Dept <http://www.uni-konstanz.de> % contact |-> URL : http://www.cs.bham.ac.uk/~fauserb/ % Phone : +44-121-41-42795 -- 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.
