The world of Chu according to Pavlovic

Steve Lack – 23 October 1996

In Ross Street's talk Barr's paper on ` `The Chu construction'' two weeks ago, the question arose as to what was the universal property of this construction. I described today the answer given in Dusko Pavlovic, Chu I: cofree equivalences, dualities and *-autonomous categories. (Note: the link is to a gzipped postscript file.) There are two 2-categories introduced there, whose objects are the *-autonomous categories, and the closed symmetric monoidal categories with a designated object. There is a forgetful 2-functor which takes a *-autonomous category to the underlying closed symmetric monoidal category with I* (which is the dualizing object in the *-autonomous category) as designated object. The Chu construction then gives a right adjoint to this forgetful functor.