On Sun, May 24, 2009 at 4:30 PM, David Roe <[email protected]> wrote: > >> >> >> 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.
Why? Why do you think elements can't be objects in a category? -- William --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
