## When is a Frobenius monoidal functor a Frobenius monoid?

### Micah Blake McCurdy – 9 March 2011

We tenuously connect three results:

1) Jeff Egger has developed a construction of functor categories
between star-autonomous categories which specialises to cover
linearly-distributive categories in some cases.

2) Craig Pastro and Ross Street have shown that, for F a separable
frobenius monoid in a braided monoidal category, there is a weak
bialgebra structure on the tensor product of F with itself.

3) In my thesis, I show that every separable Frobenius monoidal
functor gives rise to a weak-bialgebra in its codomain.

Modulo some technical wrinkles which we will discuss, it appears as
though the Tannaka construction of 3) can be obtained as a composite
of processes 1) and 2).

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