ISSN 1201-561X

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THEORY AND APPLICATIONS OF CATEGORIES

Volume 26, 2012

Kan extensions and lax idempotent pseudomonads F. Marmolejo and R.J. Wood 1

On the iteration of weak wreath products Gabriella Böhm 30

On diagram-chasing in double complexes George M. Bergman 60

Commutative monads as a theory of distributions Anders Kock 97

Closed categories vs. closed multicategories Oleksandr Manzyuk 132

Syntactic characterizations of properties of classifying toposes Olivia Caramello 176

Note on star-autonomous comonads Craig Pastro 194

A characterization of representable intervals Michael A. Warren 204

Graphical Methods for Tannaka duality of weak bialgebras and weak Hopf algebras Micah Blake McCurdy 232 Notes on Bimonads and Hopf Monads Bachuki Mesablishvili and Robert Wisbauer 281

\begin{matrix}c \\ ◯ \end{matrix} The Editors of Theory and Applications of Categories 2012. Permission to copy for private use

granted.

The coalgebraic structure of cell complexes Thomas Athorne 304

Congruences of Morita equivalent small categories Valdis Laan 331

Injective hulls of partially ordered monoids J. Lambek, Michael Barr, John F. Kennison, R. Raphael 338

Biequivalences in tricategories Nick Gurski 349

Skew monoidales, skew warpings and quantum categories Stephen Lack and Ross Street 385

A presheaf interpretation of the generalized Freyd conjecture Anna Marie Bohmann and J. P. May 403

Range categories I: General theory J.R.B. Cockett, Xiuzhan Guo and Pieter Hofstra 412

Range categories II: Towards regularity J.R.B. Cockett, Xiuzhan Guo and Pieter Hofstra 453

Opetopes and chain complexes Richard Steiner 501

Modeling stable one-types Niles Johnson, Anglica M. Osorno 501

Yoneda representations of flat functors and classifying toposes Olivia Caramello 538

Bimonadicity and the explicit basis property Matias Menni 554

Duality and traces for indexed monoidal categories Kate Ponto and Michael Shulman 582 Isotropy and crossed toposes Jonathon Funk, Pieter Hofstra and Benjamin Steinberg 660

Site characterizations for geometric invariants of toposes Olivia Caramello 710

Span, cospan, and other double categories Susan Niefield 729

Tangled circuits R. Rosebrugh, N. Sabadini and R. F. C. Walters 743

Décalage and Kan’s simplicial loop group functor Danny Stevenson 533

Internal categories, anafunctors and localisations David Michael Roberts 768

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

Valeria de Paiva: valeria.depaiva@gmail.com

Ezra Getzler, Northwestern University: getzler(at)northwestern(dot)edu Kathryn Hess, Ecole Polytechnique Fédérale de Lausanne: kathryn.hess@epfl.ch Martin Hyland, University of Cambridge: M.Hyland@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 Edinburgh: Tom.Leinster@ed.ac.uk Ieke Moerdijk, Radboud University Nijmegen: i.moerdijk@math.ru.nl Susan Niefield, Union College: niefiels@union.edu Robert Paré, Dalhousie University: pare@mathstat.dal.ca Jiri Rosicky, Masaryk University: rosicky@math.muni.cz Giuseppe Rosolini, Università di Genova: rosolini@disi.unige.it Alex Simpson, University of Edinburgh: Alex.Simpson@ed.ac.uk James Stasheff, University of North Carolina: jds@math.upenn.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: rfcwalters@gmail.com R. J. Wood, Dalhousie University: rjwood@mathstat.dal.ca