I agree that we shouldn't have Groups.blah since the static methods 
become methods/attributes of Groups() (we can see this behavior with 
Partitions.from_*`\) and would clutter up the category's methods. Perhaps 
they could be accessible via a static attribute Groups.objects (Nicolas and 
I talked about this a little bit on http://trac.sagemath.org/ticket/15882)?

I'm liking the groups.Category() since the subcategories are accessible via 
the axioms (with #10963).

For multiple implementations, we'll take an `implementation` keyword if the 
input doesn't force a particular implementation (other parts of Sage do 
this, e.g. FreeAlgebra).

Best,
Travis

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