On endomorphism algebras of separable monoidal functors

Brian Day and Craig Pastro

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.

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