Hi Bill, On Mon, Nov 10, 2008 at 9:31 PM, Bill Page <[EMAIL PROTECTED]> wrote: >> The current design should leave the door open for those who will >> want to do category theory (i.e. calculations on the categories >> themselves), rather than using them to organize generic code which >> is my own main goal. > > This strategy also conflicts strongly with my personal vision of how > mathematical category theory (as opposed to "category" as implemented > in Axiom and Sage) ought to fit into computer algebra. Category theory > has rapidly become an essential part of the toolkit of the computer > scientist. It has also gained almost universal acceptance in > mathematics as at least one of the ways in which mathematics can be > accurately and formally presented. Most aspects of category theory are > essentially algebraic in nature. So it seems peculiar in the extreme > to me that almost all computer algebra systems treat category theory > as at best a kind of "add-on" rather than a fundamental design > approach. > > It seems to me that of all the existing computer algebra systems, > because of it's strong and often pedantic type system, Axiom seems > most compatible with taking category theory as a foundation. > Unfortunately in most respects Axiom does not do nearly enough to > exploit this. Magma apparently also takes a formal approach that is at > least in part motivated by category theory but I was rather > disappointed to see how little of this remains in the approach now > implemented in Sage.
Just a quick note. Categories in Sage are modeled after the mathematical categories rather than Ralf's universal algebra notion. That is, you have objects, morphisms, functors, homsets, etc. They just happen to be a convenient place to put generic methods for their objects. --Mike --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
