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

Published online by Cambridge University Press:  01 February 1997

DUšKO PAVLOVIĆ
Affiliation:
Present address: COGS, University of Sussex, Brighton BN1 9QH, UK. Department of Computing, Imperial College, London SW7 2BZ, UK

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.

Type
Research Article
Copyright
© 1997 Cambridge University Press

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