+1 to a catalog (using lazy imports as much as possible!)
+1 to removing not-very-common categories from global namespace

Not convinced about the alias AdditiveCommutativeGroups =
CommutativeAdditiveGroups. I believe it will just add confusion, and
wildcards are our friends (as in *AdditiveGroups*?). Besides, as was
mentioned, one can already get something close with
AdditiveGroups().AdditiveCommutative()

Open question: do we want the catalog to contain things like the short
hands CommutativeRings(), when we already have Rings().Commutative()?
When I implemented axioms, I left CommutativeRings around mostly with
backward compatibility in mind.

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

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