> > >> Bill Page wrote: > >>> How does it related to the concept of "parent" - which seems equally > >>> ill-defined to me? > > > On Jun 3, 2008, at 10:04 PM, Robert Bradshaw wrote: > >> A Parent is an Object in the category of Sets, > > David Harvey wrote: > > huh? Don't you mean to say something more like "a parent is an object > > of a concrete category", i.e. a category C with a faithful functor > > f : C -> Set, such that the "elements" (as understood by Sage) of the > > parent P are exactly the elements of f(P)? > > I rather like David's definition because it is careful to make a > connection to category theory. Unfortunately, as far as I can tell > Sage does not directly implement this notion. I mean: there is no such > identifiable concrete category in Sage as such, even if it is true > that a parent "behaves" in this manner. In any case, perhaps it would > be helpful if 'parent' was replaced with
I still like the name parent, but I agree with David's definition (and have recently written basically the same thing in the documentation for the category patch): a parent is an object in a concrete category. Currently it inherits from CategoryObject, which implements an arbitrary object (not necessarily in a concrete category). > sage: concrete_category(1) > Integer Ring > > But there is a further complication since there already is some kind > of "category" associated with elements: > > sage: category(1) > Category of elements of Integer Ring > > I do not understand what this really is yet. It does not seem to me > that the elements of Integer Ring actually form a category as such. > My understanding was that this dates from when Sage tried to give every object a category. I think it should change: elements don't have a category, their parents do. David --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
