On Sun, May 24, 2009 at 7:55 PM, William Stein wrote: > > On Sun, May 24, 2009 at 4:47 PM, David Roe wrote: >> Primarily because it's not clear what the morphisms are. At least, I don't >> think that elements should default to a category of all elements of their >> parent with trivial morphisms: I don't see that as being useful. >> >> Now, it's certainly true that one can have categories where the objects are >> usually represented by elements in Sage. But I'd say that the best way to >> implement the category with objects the positive integers and a unique >> morphism from m to n if m divides n would be to create a new class >> inheriting from CategoryObject, given an integer at runtime. > > OK, so you just don't want elements to be objects in a category by > *default*. However, if one does a little more work then elements > can be objects in a category. That sounds reasonable to me. >
But none of this has much to do with category theory as such where normally elements of some co-domain are *morphisms* with the domain some terminal object in the category. Regards, Bill Page. --~--~---------~--~----~------------~-------~--~----~ 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/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
