Chu I: cofree equivalences, dualities and *-autonomous categories

Authors:
Duško Pavlović
Affiliations:
Department of Computing, Imperial College, London SW7 2BZ, UK
Venue:
Mathematical Structures in Computer Science
Year:
1997

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Abstract

We study three comonads derived from the comma construction. The induced coalgebras correspond to the three concepts displayed in the title of the paper. The comonad that yields the *-autonomous categories is, in essence, the Chu construction, which has recently awaken much interest in computer science. We describe its couniversal property. It is right adjoint to the inclusion of *-autonomous categories among autonomous categories, with lax structure-preserving morphisms. Moreover, this inclusion turns out to be comonadic: *-autonomous categories are exactly the Chu-coalgebras.