On Mon, Jun 24, 2013 at 02:22:18PM -0700, Jean-Baptiste Priez wrote:
>    I push in the queue a simple patch about the categories with axioms for
>    NCSF-QSym and SF and I try to do tests:
>    And...

I am not sure what's your point. Is this a call for help?

I had a quick look at the patch. You want:

        GradedHopfAlgebras(R).Commutative().Realizations().WithBasis()

instead of

        GradedHopfAlgebras(R).Commutative().WithBasis().Realizations()

It's a not a realization of 'an algebra with a basis', but 'a
realization of an algebra' with a basis.

While you are at it, you might want to use:

        
HopfAlgebras(R).Graded().Connected().Commutative().Realizations().WithBasis()

Oh and this is actually still missing a piece of information; namely
that the basis is compatible with the grading:

        HopfAlgebras(R).Graded().Connected().Commutative().Realizations()
        & Modules(R).WithBasis().Graded()

Hmm, this is not as nice as it could be. One thing to check as well is
that a realization of a commutative thingy is indeed commutative, and
similarly for graded connected; I am not sure this is already
implemented.

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

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