Nicolas,
How about this from sage.categories.modules_with_basis.
--Mark
{{{
class TensorProducts(TensorProductsCategory):
"""
The category of modules with basis constructed by tensor product of
modules with basis.
"""
@cached_method
def extra_super_categories(self):
"""
EXAMPLES::
sage:
ModulesWithBasis(QQ).TensorProducts().extra_super_categories()
[Category of modules with basis over Rational Field]
sage: ModulesWithBasis(QQ).TensorProducts().super_categories()
[Category of modules with basis over Rational Field]
"""
return [self.base_category()]
}}}
> On Thu, Apr 03, 2014 at 08:19:16AM -0400, Mark Shimozono wrote:
> > Here is an example. I think the problem is that the tensor
> > covariant construction functor stores the base category as an attribute
> > before the QQ-module ---> QQ-vector-space category mangling occurs.
> >
> > --Mark
> >
> > {{{
> >
> > sage: A=CombinatorialFreeModule(QQ,[1])
> > sage: B=CombinatorialFreeModule(QQ,[2])
> > sage: AB = tensor([A,B])
> > sage: BA = tensor([B,A])
> > sage: f = AB.module_morphism(on_basis=lambda (x,y):
> > BA.monomial((y,x)), codomain=BA, category=ModulesWithBasis(QQ))
> > Traceback (most recent call last):
> > ...
> > TypeError: Free module generated by {1} over Rational Field # Free
> > module generated by {2} over Rational Field is not in Category of vector
> > spaces with basis over Rational Field
> >
> > }}}
>
> Ok, thanks! That's the same issue as we had recently: the tensor
> construction is supposed to be regressive but it's not implemented as
> such. Namely, C.TensorProducts() should always include C as super
> category, which is not the case above:
>
> sage: AB in VectorSpaces(QQ)
> False
>
> That's independent of the mangling for Modules.
>
> Cheers,
> Nicolas
> --
> Nicolas M. Thiéry "Isil" <nthi...@users.sf.net>
> http://Nicolas.Thiery.name/
>
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