On Tue, May 27, 2014 at 09:14:03PM +0200, Vincent Delecroix wrote:
> A module over ZZ is the same thing as an Abelian group. Why do we have
> two distinct categories ?

This issue is mentioned on http://trac.sagemath.org/wiki/CategoriesRoadMap.

So far, the two categories have not been merged for a stupid
bootstrapping reason: to construct Modules(ZZ), we need to construct
ZZ. To construct ZZ, an abelian group, we need to construct the
category CommutativeAdditiveGroups(). So if the latter is an alias for
Modules(ZZ), we are stuck.

This is basically the same reason why QQ is not in Algebras(QQ) [1]

It might be possible to break the loop with some lazyness. If someone
cares enough to investigate, please!

Cheers,
                                Nicolas

[1] For that one, thanks to #15801, we could possibly put QQ in
Algebras(Fields()) if we believe this is useful. But not yet have
Fields() be a subcategory of Algebras(Fields()).

--
Nicolas M. ThiƩry "Isil" <nthi...@users.sf.net>
http://Nicolas.Thiery.name/

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