ISSN 1201-561X

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THEORY AND APPLICATIONS OF CATEGORIES

Volume 18, 2007

Bicat is not triequivalent to Gray Stephen Lack 1

Polarized category theory, modules, and game semantics J.R.B. Cockett and R.A.G. Seely 4

Functional analysis on normed spaces: the Banach space comparison M. Sioen and S. Verwulgen 102

On Yetter’s Invariant and an Extension of the Dijkgraaf-Witten Invariant to Categorical Groups Joao Faria Martins and Timothy Porter 118

Pullback and finite coproduct preserving functors between categories of permutation representations: Corrigendum and Addendum Elango Panchadcharam and Ross Street 151

CCD lattices in presheaf categories G. S. H. Cruttwell, F. Marmolejo and R.J. Wood 157

Monad compositions I: general constructions and recursive distributive laws Ernie Manes and Philip Mulry 172

Quasi locally connected toposes Marta Bunge and Jonathon Funk 209 More morphisms between bundle gerbes Konrad Waldorf 240

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Towards an n-category of cobordisms Eugenia Cheng and Nick Gurski 274

The theory of core algebras: its completeness Peter Freyd 303

Higher cospans and weak cubical categories (Cospans in algebraic topology, I) Marco Grandis 321

Coherent unit actions on regular operads and Hopf algebras Kurusch Ebrahimi-Fard and Li Guo 348

Dense morphisms of monads Panagis Karazeris and Jiri Velebil 372

Enriched model categories and an application to additive endomorphism spectra Daniel Dugger and Brooke Shipley 400

Nuclei of categories with tensor products Alexei Davydov 440

Exploring the gap between linear and classical logic Francois Lamarche 473

On the axiomatisation of Boolean categories with and without medial Lutz Strassburger 536

Collared cospans, cohomotopy and TQFT (cospans in algebraic topology, II) Marco Grandis 602

A universal property of the monoidal 2-category of cospans of ordinals and surjections M. Menni, N. Sabadini and R. F. C. Walters 631

Quotients of tannakian categories J.S. Milne 654

Familial 2-functors and parametric right adjoints Mark Weber 665

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. The method of distribution of the journal is via the Internet tools WWW/ftp. The journal is archived electronically and in printed paper format.

Subscription information. Individual subscribers receive (by e-mail) abstracts of articles as they are published. Full text of published articles is available in .dvi, Postscript and PDF. Details will be e-mailed to new subscribers. 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 the preferred flavour. TEX source of articles for publication should be submitted by e-mail directly to an appropriate Editor. They are listed below. Please obtain detailed information on submission format and style files from the journal’s WWW server at http://www.tac.mta.ca/tac/. You may also write to tac@mta.ca to receive details by e-mail.

Editorial board.

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

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

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, Xerox Palo Alto Research Center: paiva@parc.xerox.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 G. Max Kelly, University of Sydney: maxk@maths.usyd.edu.au 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