On Mon, Mar 24, 2014 at 04:35:49PM -0400, Mark Shimozono wrote:
> Here is a probably unintended consequence of
> rewriting ModulesWithBasis(QQ) in terms of vector spaces,
>
> --Mark
>
> {{{
>
> sage: cat = ModulesWithBasis(QQ); cat
> Category of vector spaces with basis over Rational Field
>
> sage: cat2 = ModulesWithBasis(QQ).TensorProducts().base_category(); cat2
> Category of modules with basis over Rational Field
>
> sage: cat == cat2
> False
>
> }}}
This rewriting is indeed a bit crappy in general Modules ought to be a
functorial construction.
That being aid, in the case at hand, it's a general behavior whenever
a specific category does not implement anything about a given
functorial construction:
sage: Groups().CartesianProducts().base_category()
Category of monoids
The advantage is that this avoid creating lots of intermediate
categories. The inconvenient is that we are loosing information. In
the case of covariant functorial constructions, we could indeed do
better at not much cost by returning the intersection of the above
with the category of groups. I'll keep that in mind.
Cheers,
Nicolas
--
Nicolas M. Thiéry "Isil" <nthi...@users.sf.net>
http://Nicolas.Thiery.name/
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