The Conference "Category Theory '90" was held in Como (Italy) from July 22 to July 28, 1990. The organizing committee was composed of: A. Carboni, University of Milan, Italy M.C. Pedicchio, University of Trieste, Italy G. Rosolini, University of Parma, Italy. The scientific committee was composed of: J. Adamek (Prague), J. Benabou (Paris), A. Heller (New York), P.T. Johnstone (Cambridge), G.M. Kelly (Sydney), F. W. Lawvere (Buffalo). 125 persons took part to the Conference and 46 of them gave a talk. The editors would like to express their gratitude to the organisms that supported the meeting: "Consiglio Nazionale delle Ricerche" "Gruppi Nazionali 40% di Topologia e Logica" Universities of Milan, Parma and Trieste, as well as to all referees for their competent and prompt collaboration and to Springer for publishing the Proceedings.
The volume is divided in two parts: the first one contains research papers and is preceded by an introductory article by F. W. Lawvere; the second part consists of a monograph by A. Joyal and R. Street on Tannaka duality and quantum groups. It is intended to be an introduction to this rapidly growing subject and is addressed to a wider audience than category theorists; the paper is not only expository, but also contains new results and new proofs of classical results.