ISSN 1201-561X

[figure: T; A; C]

THEORY AND APPLICATIONS OF CATEGORIES

Volume 20, 2008

Editorial Notice: Max Kelly, 5 June 1930 - 26 January 2007 Ross Street 1

Locally cartesian closed categories without chosen constructions Erik Palmgren 5

Generalized Brown representability in homotopy categories: Erratum Jiri Rosicky 18

Frobenius objects in cartesian bicategories R.F.C Walters and R.J. Wood 25

Abelian groupoids and non-pointed additive categories Dominique Bourn 48

Coherence for pseudodistributive laws revisited F. Marmolejo and R. J. Wood 74

Balanced category theory Claudio Pisani 85

Category-theoretic models of linear Abadi and Plotkin logic Lars Birkedal and Rasmus E. Mogelberg and Rasmus L. Petersen 116 Kan extensions in double categories (On weak double categories, Part III) Marco Grandis and Robert Paré 152

\begin{matrix}c \\ ◯ \end{matrix} The Editors of Theory and Applications of Categories 2008. Permission to copy for private use

granted.

Fundamental pushout toposes Marta Bunge 186

Algebraic real analysis Peter Freyd 215

Star-autonomous functor categories Jeff Egger 307

Colimits of representable algebra-valued functors George M. Bergman 334

Quotients of unital A_{∞}-categories Volodymyr Lyubashenko and Oleksandr Manzyuk 405

Core varieties, extensivity, and rig geometry F. William Lawvere 497

Isbell duality Michael Barr, John F. Kennison, and R. Raphael 504

Cohomology theory in 2-categories Hiroyuki Nakaoka 542

Propriétés universelles et extensions de Kan dérivées Denis-Charles Cisinski 605

Framed bicategories and monoidal fibrations Michael Shulman 650

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.

Full text of the journal is freely available in .dvi, Postscript and PDF from the journal’s server at http://www.tac.mta.ca/tac/ and by ftp. It is archived electronically and in printed paper format.

Subscription information. Individual subscribers receive by e-mail abstracts of articles by e-mail as they are published. To subscribe, send e-mail to tac@mta.ca including a full name and postal address. For institutional subscription, send enquiries to the Managing Editor.

Information for authors. The typesetting language of the journal is TEX, and L^{A}TEX 2ε is strongly encouraged. Articles should be submitted by e-mail directly to a Transmitting Editor. Please obtain detailed information on submission format and style files from http://www.tac.mta.ca/tac/.

Managing editor. Robert Rosebrugh, Mount Allison University: rrosebrugh@mta.ca

TEXnical editor. Michael Barr, McGill University: barr@math.mcgill.ca

Assistant TEX editor. Gavin Seal, McGill University: gavin seal@fastmail.fm

Transmitting editors.

Richard Blute, Université d’ Ottawa: rblute@uottawa.ca Lawrence Breen, Université de Paris 13: breen@math.univ-paris13.fr Ronald Brown, University of North Wales: ronnie.profbrown (at) btinternet.com Aurelio Carboni, Università dell Insubria: aurelio.carboni@uninsubria.it Valeria de Paiva, Cuill Inc.: valeria@cuill.com Ezra Getzler, Northwestern University: getzler(at)northwestern(dot)edu Martin Hyland, University of Cambridge: M.Hyland@dpmms.cam.ac.uk P. T. Johnstone, University of Cambridge: ptj@dpmms.cam.ac.uk Anders Kock, University of Aarhus: kock@imf.au.dk Stephen Lack, University of Western Sydney: s.lack@uws.edu.au F. William Lawvere, State University of New York at Buffalo: wlawvere@acsu.buffalo.edu Jean-Louis Loday, Université de Strasbourg: loday@math.u-strasbg.fr Ieke Moerdijk, University of Utrecht: moerdijk@math.uu.nl Susan Niefield, Union College: niefiels@union.edu Robert Paré, Dalhousie University: pare@mathstat.dal.ca Jiri Rosicky, Masaryk University: rosicky@math.muni.cz Brooke Shipley, University of Illinois at Chicago: bshipley@math.uic.edu James Stasheff, University of North Carolina: jds@math.unc.edu Ross Street, Macquarie University: street@math.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 Insubria: robert.walters@uninsubria.it R. J. Wood, Dalhousie University: rjwood@mathstat.dal.ca