On Aug 28, 5:38 am, "Nicolas M. Thiery" <nicolas.thi...@u-psud.fr>
wrote:

> What remains to be done is to find a good set of names to distinguish
> between the two feature sets.
>
>  - The ambiguity is mostly for direct sum, right?

I think so.

>  - Are there (useful) cases where the direct product of a subcategory
>    of Sets does not coincide with the cartesian product on the
>    underlying sets?

Not that I can think of right now.

>  - There could be some ambiguity for tensor product which is often
>    used as an alias for cartesian product for graphs, crystals, ...
>    But those are not subcategories of VectorSpaces/Modules. So it
>    would not be an issue to have a similar alias in Sage.

That sounds okay to me.

I think that "cartesian_product" is a good, unambiguous (I think) name
for the set construction. "direct_sum" and "direct_product" are maybe
okay, while definitely "coproduct" and possibly "product" should be
reserved for the category-level operation.

  John

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