id,summary,reporter,owner,description,type,status,priority,milestone,component,resolution,keywords,cc,work_issues,upstream,reviewer,author,merged,dependencies,stopgaps
8807,Adding support for morphisms to the category framework,SimonKing,Simon King,"Working on the doc tests for sage.category at #8800, I found that support for morphisms is missing in the category framework. I think this is important, and therefore I am opening this ticket.

Some thoughts on implementing support.

Let f be a morphism in a category C, and let F be a functor, F.domain()==C. Then F(f) should by default try F(f.domain()).hom(f,F(f.codomain())). This relies on the call method of F(f.domain()).Hom(F.codomain()), which in turn uses _coerce_impl. I think it is there where the support should be implemented.

Example:

In sage.rings.homset.RingHomset_generic_with_category._coerce_impl, one has
{{{
        ...
        if x.parent() == self:
            if isinstance(x, morphism.RingHomomorphism_im_gens):
                return morphism.RingHomomorphism_im_gens(self, x.im_gens())
            elif isinstance(x, morphism.RingHomomorphism_cover):
                return morphism.RingHomomorphism_cover(self)
        raise TypeError
}}}
Why not instead
{{{
        try:
            if isinstance(x, morphism.RingHomomorphism_im_gens):
                return morphism.RingHomomorphism_im_gens(self, x.im_gens())
            elif isinstance(x, morphism.RingHomomorphism_cover):
                return morphism.RingHomomorphism_cover(self)
        except:
            raise TypeError
}}}

If I do so, the following works:
{{{
sage: R.<x> = QQ[]
sage: f = R.hom([2*x],R)
sage: C = Fields()
sage: f2 = C(R).hom(f,C(R))
sage: f2
Ring endomorphism of Fraction Field of Univariate Polynomial Ring in x over Rational Field
  Defn: x |--> 2*x
sage: f2(1/x)
1/(2*x)
}}}

It should be straight forward to change the call method of ``C`` so that ``C(f)`` reproduces the above construction. Similarly, if ``F`` is a functor then ``F(f)`` should call ``F(f.domain()).hom(f,F(f.codomain()))``.",enhancement,closed,major,sage-4.6.2,categories,fixed,morphisms functors categories,kohel was wdj robertwb,,N/A,John Cremona,Simon King,sage-4.6.2.alpha0,,