ISSN 1201-561X

[figure: T; A; C]

THEORY AND APPLICATIONS OF CATEGORIES

Volume 24, 2010

Bicategories of spans as cartesian bicategories Stephen Lack, R.F.C. Walters, and R.J. Wood 1

The Frobenius relations meet linear distributivity J.M. Egger 25

Joyal’s arithmetic universe as list-arithmetic pretopos Maria Emilia Maietti 39

Monads as extension systems - no iteration is necessary F. Marmolejo and R. J. Wood 84

On a conjecture by J.H.Smith George Raptis 114

Topos theoretic aspects of semigroup actions Jonathon Funk and Pieter Hofstra 117

Transversal homotopy theory Jonathan Woolf 148

On modified Reedy and modified projective model structures Mark W. Johnson 179

Finitely presentable morphisms in exact sequences Michel Hbert 209 The Hopf algebra of Mbius intervals F. W. Lawvere and M. Menni 221

\begin{matrix}c \\ ◯ \end{matrix} The Editors of Theory and Applications of Categories 2010. Permission to copy for private use

granted.

Tensor products of sup-lattices and generalized sup-arrows T. Kenney and R.J. Wood 266

Lax presheaves and exponentiability Susan Niefield 288

The span construction Robert Dawson, Robert Paré, Dorette Pronk 302

On *-autonomous categories of topological modules Michael Barr, John F. Kennison, and R. Raphael 378

A logic for categories Claudio Pisani 394

On the duality between trees and disks David Ouryn 418

Internal profunctors and commutator theory; applications to extensions classification and categorical Galois Theory Dominique Bourn 451

Higher Dimensional Algebra VII: Groupoidification John C. Baez, Alexander E. Hoffnung, and Christopher D. Walker 489

Hopf monoidal comonads Dimitri Chikhladze, Stephen Lack, and Ross Street 554

Strictification of categories weakly enriched in symmetric monoidal categories Bertrand J. Guillou 564

A unified framework for generalized multicategories G.S.H. Cruttwell and Michael A. Shulman 580

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, Ecole Polytechnique Fédérale de Lausanne:

gavin seal@fastmail.fm

Transmitting editors.

Clemens Berger, Université de Nice-Sophia Antipolis, cberger@math.unice.fr 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: valeria.depaiva@gmail.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, Macquarie University: steve.lack@mq.edu.au F. William Lawvere, State University of New York at Buffalo: wlawvere@buffalo.edu Tom Leinster, University of Glasgow, Tom.Leinster@glasgow.ac.uk 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