We show that the (co)endomorphism algebra of a sufficiently separable ``fibre'' functor into $Vect_k$, for $k$ a field of characteristic 0, has the structure of what we call a ``unital'' von Neumann core in $Vect_k$. For $Vect_k$, this particular notion of algebra is weaker than that of a Hopf algebra, although the corresponding concept in $Set$ is again that of a group.
Keywords: separable fibre functor, Tannaka reconstruction, bialgebra, von Neumann core
2000 MSC: 18D99, 16B50
Theory and Applications of Categories,
Vol. 22, 2009,
No. 4, pp 77-96.
http://www.tac.mta.ca/tac/volumes/22/4/22-04.dvi
http://www.tac.mta.ca/tac/volumes/22/4/22-04.ps
http://www.tac.mta.ca/tac/volumes/22/4/22-04.pdf
ftp://ftp.tac.mta.ca/pub/tac/html/volumes/22/4/22-04.dvi
ftp://ftp.tac.mta.ca/pub/tac/html/volumes/22/4/22-04.ps