Chu. I: Cofree equivalences, dualities and *-autonomous categories (Q2785695)

The Chu construction yields, for any fixed object \(\perp\) of an autonomous category, a *-autonomous category, with \(\perp\) its dualizing object [see \textit{M. Barr}, Lect. Notes Math. 752 (1979; Zbl 0415.18008), Appendix by \textit{P.-H. Chu}]. The author's main result is that this construction is the object part of a right adjoint to the inclusion functor of the (very naturally defined) 2-categories in question, and that this functor is comonadic. His proof is based on an interpretation of the Chu construction as a comma construction, and on a more general result which presents the comma construction as a right adjoint to the inclusion functor \{self adjunctions\} \(\hookrightarrow\) \{dualities\}. The author also states that a similar result may be obtained for the Hyland-de Paiva Dialectica categories [see \textit{V. C. V. de Paiva}, Contemp. Math. 92, 47-62 (1989; Zbl 0675.03039)].