> > I guess FiniteDimensionalAlgebrasWithBasis has both the old Algebras() > > and the new MagmaticAlgebras() as supercategories? That would explain > > why I'm seeing associativity and rings everywhere. > > > > ...and building up a pile of non-associative categories one-at-a-time > doesn't work either, of course =) > > MagmaticAlgebras has been around for quite some time. At some point, there is a plan to make Algebras to not assume associativity in order to be more explicit. Also, Algebras is not "old" and not going away. However, as you said, FiniteDimensionalAlgebrasWithBasis has Algebras as a basis, and so it is associative. For the analogous thing, you want MagmaticAlgebras(R).FiniteDimensional().WithBasis() (maybe also .Unital() added too). However, this will be a more generic join category. If some of the methods currently in the associative version still apply, you should create the corresponding category and move those methods to this category. Does that clarify things?
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