Dear Paul, My PhD thesis covers a construction for dagger categories in 3.1.18 and further that is slightly different but related; at least I also called this functor Zigzag:Cat->DagCat. In that case, it is left adjoint to the evident forgetful functor. best, Chris
For a set A, let Cat(A) be the category whose objects are small categories with object set A, and whose morphisms are identity-on- objects functors.
For a small category C, let zigzag(C) be the coproduct of C and C^op within Cat(ob C).
Explicitly, in zigzag(C), a non-identity morphism z : a ---> b is a nonempty sequence of non-identity C-morphisms that alternately go forwards or backwards. Depending on the direction of the first and last C-morphism, z can take one of four different forms.
Surely this appears in the literature? Google gave me a zillion categorical papers that mention zigzags, but I didn't find this construction, although several were close (e.g. the special case where C is the free category on a graph).
Paul
-- Paul Blain Levy School of Computer Science, University of Birmingham +44 (0)121 414 4792 http://www.cs.bham.ac.uk/~pbl
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