On Wed, Apr 28, 2010 at 9:51 AM, Simon King <simon.k...@nuigalway.ie> wrote: > Hi! > > I always thought that categories and functors are about objects *and* > morphisms. But is this implemented in the categories of Sage? > > Example: > sage: R.<x> = ZZ[] > sage: f = R.hom([2*x],R) > sage: C = Fields() > sage: R in C # R is no field, so its fine: > False > sage: f in C.hom_category() # ?? > True > sage: C.hom_category() > Category of hom sets in Category of rings > > So, the fields do not have their own hom category, and instead use > ring homomorphisms. > > Now about functors. The fraction field construction is functorial, and > indeed one has > sage: F = C(R) > sage: F > Fraction Field of Univariate Polynomial Ring in x over Integer Ring > > But if it is a functor, I would expect that in some way one is able to > transform f into the corresponding automorphism of F. > > Is this implemented in Sage? I expected that C(f) would return a > morphism, but it only yields an error. And while > sage: f2 = C.hom_category()(f) > does not raise an error, one has > sage: f2 is f > True > so, this is not what I was looking for. > > f.extend_codomain(F).extend_domain(F) or F.hom(f,F) doesn't work > either. Another failing attempt was to work with a proper functor, > namely > sage: Frac = F.construction()[0] > sage: Frac > FractionField > sage: Frac(R) is F > True > sage: Frac(f) > *BOOM* > > So, what can one do? Is there the framework to implement the missing > bits? When I look at the code in sage/categories/functor.pyx, it seems > that morphisms are not taken care of.
The T-shirt I'm wearing says -- "It's easy. Implement it and post a patch." But seriously, the above is natural and makes sense, but is *NOT* implemented. It would be a great thing for people to make a stab at. It would be very good to get feedback from Nick A., Robert B., Nick T., etc. -- William > > Best regards, > Simon > > -- > To post to this group, send email to sage-support@googlegroups.com > To unsubscribe from this group, send email to > sage-support+unsubscr...@googlegroups.com > For more options, visit this group at > http://groups.google.com/group/sage-support > URL: http://www.sagemath.org > -- William Stein Professor of Mathematics University of Washington http://wstein.org -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
