Nicolas,
In short, the category code has a number of problems due to the
many joins that are appearing because of Module-over-field =
vectorspace-over-field.
--Mark
> I put in that line you suggested for VectorSpaces.TensorProducts().
>
> The categories that are appearing now tend to be Joins.
>
> I tried
>
> {{{
>
> sage: ModulesWithBasis(QQ).TensorProducts().base_ring()
> Traceback (most recent call last)
> ...
> AssertionError: some subcategory of Join of Category of tensor products of
> modules with basis over Rational Field and Category of tensor products of
> vector spaces over Rational Field should be a category over base ring
>
> }}}
>
> There doesn't seem to be an obvious way to get the base_ring in general.
> The category might be a join, the supercategories might be tensor products
> or not, etc.
>
> --Mark
>
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