John Baez could not recall whether bilax and Frobenius monoidal functors = are the same. The answer is no, in the usage I'd been familiar with, bilax meant = simply equipped with both lax and oplax structures, while a Frobenius = monoidal functor satisfies additional coherence relation which = generalize the relations between the multiplication and comultiplication = in a Frobenius algebra. A bilax monoidal functor from the one-object monoidal category to VECT = would be a vector-space with both an algebra and a coalgebra structure = on it (no coherence relations relating them), while a Frobenius monoidal = functor would be a Frobenius algebra. =20 Aguiar (with good reason), on the other hand, reserves bilax for = functors equipped with coherence relations generalizing the relations = between the operations and cooperations in a bialgebra, so that a bilax = functor from the one-object monoidal category to VECT would be a = bialgebra. This notion, however, only makes sense in the presence of = braidings on the source and target. I think Aguiar's usage should prevail, though we also need a name for = functors between general monoidal categories which are simultaneously = lax and oplax. Best Thoughts, David Yetter= [For admin and other information see: http://www.mta.ca/~cat-dist/ ]