Re: evil (fwd)

[Dusko Pavlovic <Dusko.Pavlovic@comlab.ox.ac.uk>]

the definition that i proposed was overconstrained. it should be:

>> DEF. Let CC be a monoidal category. a *dagger* on CC is a functor
>> P: CC^op ---> CC which is
>>
>> * self-adjoint
>> * equivalence
>> * given together with the maps (*not* necessarily dinatural)
>> ** e_X : X (x) PX ---> I
>> ** h_X : I--->PX (x) X
>> which make PX -| X.

if e_X and h_X happen to be dinatural, then P is just the star functor. in
general, all we know about P is that it is a functor whose object part
maps each object to some dual. the idea is that in the case of FHilb, we
can take P to be the functor which will take a linear operator f:A-->B to
the conjugate of the dual operator. to get the adjoint operator
f^dag:B-->A, tranfer Pf:B*-->A* along the isomorphisms A~A* and B~B*,
induced by the frobenius structures on A and B.

sorry about the mistake, and thanks for pointing it out.

-- dusko


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