Theory and Applications of Categories, Vol. 2, 1996, pp. 1–2.

EDITORIAL NOTICE:

ROBERT W. THOMASON, 1952-1995.

At the end of last year, the editorial board of Theory and Applications of Categories was shocked by the sad loss of one of its members, Robert W. Thomason, who died suddenly as a consequence of his diabetes.

Thomason obtained his Ph.D. from Princeton University in 1977. Subsequently, he held positions at M.I.T., the University of Chicago and the Institute for Advanced Study at Princeton, before joining the mathematics department of Johns Hopkins University in 1983. In 1989, he moved to Paris, joining the C.N.R.S. and working at Paris VII, where he stayed until he passed away on November 5, 1995.

Bob Thomason has made important contributions to category theory, K-theory and homotopy theory, and had a great influence on many people working in these and related fields. I would like to say a few words about some of the more categorical aspects of his work. For a more complete descriptions of his results, the reader is referred to the article by C. Weibel in the Notices of the American Mathematical Society.

In his thesis, Thomason observed the basic and very useful fact that the ”Grothendieck construction” for a diagram of small categories provides a model for the homotopy colimit of the corresponding diagram of spaces, and he applied this result to infinite loop spaces and K-theory [MR80b:18015]. Shortly after this, he designed a Quillen closed model structure on the category of small categories, thus tying down further the equivalence between the homotopy theories of spaces and of small categories [MR82b:18005]. In his paper “Symmetric monoidal categories model all connective spectra”, which appeared in the first volume of Theory and Applications of Categories, Thomason returns to his early interests in infinite loop space machines, and proves that the well known construction of a (-1)-connective spectrum out of a symmetric monoidal category is a “localization” (i.e. represents the stable homotopy category of such spectra as a category of fractions of the category of small symmetric monoidal categories). Recently, Thomason was working on a modification of Quillen’s homotopical algebra. He lectured on this in Utrecht in the Spring of 1995, and explained that his purpose was to weaken Quillen’s axioms for a simplicial closed model category in such a way that they are preserved by the functorcategory construction, but at the same time are still strong enough for the axiomatic development of the usual homotopical constructions. He had taken the essential steps in this project.

In discussions about our new journal, Thomason showed great interest and concern, and made many valuable suggestions. He also contributed one of his last papers to our journal.

Bob will be remembered as one of the great mathematicians of his time. Moreover, many of us will remember his friendly and generous interest in the work of young students, and his wide knowledge beyond his own field and beyond mathematics. His work and personality will inspire many generations to come of mathematicians, and of category theorists in particular.

— I. Moerdijk.

THEORY AND APPLICATIONS OF CATEGORIES (ISSN 1201-561X) will disseminate articles that significantly advance the study of categorical algebra or methods, or that make significant new contributions to mathematical science using categorical methods. The scope of the journal includes: all areas of pure category theory, including higher dimensional categories; applications of category theory to algebra, geometry and topology and other areas of mathematics; applications of category theory to computer science, physics and other mathematical sciences; contributions to scientific knowledge that make use of categorical methods.

Articles appearing in the journal have been carefully and critically refereed under the responsibility of members of the Editorial Board. Only papers judged to be both significant and excellent are accepted for publication.

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Editorial board.

John Baez, University of California, Riverside: baez@math.ucr.edu Michael Barr, McGill University: barr@triples.math.mcgill.ca Lawrence Breen, Université de Paris 13: breen@math.univ-paris13.fr Ronald Brown, University of North Wales: r.brown@bangor.ac.uk Jean-Luc Brylinski, Pennsylvania State University: jlb@math.psu.edu Aurelio Carboni, University of Genoa: carboni@vmimat.mat.unimi.it P. T. Johnstone, University of Cambridge: ptj@pmms.cam.ac.uk G. Max Kelly, University of Sydney: kelly m@maths.su.oz.au Anders Kock, University of Aarhus: kock@mi.aau.dk F. William Lawvere, State University of New York at Buffalo: mthfwl@ubvms.cc.buffalo.edu Jean-Louis Loday, Université de Strasbourg: loday@math.u-strasbg.fr Ieke Moerdijk, University of Utrecht: moerdijk@math.ruu.nl Susan Niefield, Union College: niefiels@gar.union.edu Robert Paré, Dalhousie University: pare@cs.dal.ca Andrew Pitts, University of Cambridge: ap@cl.cam.ac.uk Robert Rosebrugh, Mount Allison University: rrosebrugh@mta.ca Jiri Rosicky, Masaryk University: rosicky@math.muni.cz James Stasheff, University of North Carolina: jds@charlie.math.unc.edu Ross Street, Macquarie University: street@macadam.mpce.mq.edu.au Walter Tholen, York University: tholen@mathstat.yorku.ca Myles Tierney, Rutgers University: tierney@math.rutgers.edu Robert F. C. Walters, University of Sydney: walters b@maths.su.oz.au R. J. Wood, Dalhousie University: rjwood@cs.da.ca