ISSN 1201-561X

[figure: T; A; C]

THEORY AND APPLICATIONS OF CATEGORIES

Volume 28, 2013

The monoidal structure of strictification Nick Gurski 1

Free products of higher operad algebras Mark Weber 24

Duality for distributive spaces Dirk Hofmann 66

Semiunital semimonoidal categories (Applications to semirings and semicorings) Jawad Abuhlail 123

On the monad of internal groupoids Dominique Bourn 150

Tannaka duality and convolution for duoidal categories Thomas Booker and Ross Street 166

Traced *-autonomous categories are compact closed Tams Hajgat and Masahito Hasegawa 206

Tightly bounded completions Marta Bunge 213

Geometric morphisms of realizability toposes Peter Johnstone 241 Diagonal model structures J.F. Jardine 250

\begin{matrix}c \\ ◯ \end{matrix} The Editors of Theory and Applications of Categories 2013. Permission to copy for private use

granted.

Homotopy theories of diagrams J.F. Jardine 269

n-tuple groupoids and optimally coupled factorizations Dany Majard 304

Codensity and the ultrafilter monad Tom Leinster 332

No-iteration pseudomonads F. Marmolejo and R.J. Wood 371

Tensors, monads and actions Gavin J. Seal 403

Bounded Archimedean l-algebras and Gelfand-Neumark-Stone duality Guram Bezhanishvili, Patrick J. Morandi, Bruce Olberding 435

Connections on non-Abelian gerbes and their holonomy Urs Schreiber and Konrad Waldorf 476

Subgroupoids and quotient theories Henrik Forssell 541

Sur les types d’homotopie modliss par les ∞-groupoides stricts Dimitri Ara 552

Categories enriched over a quantaloid: Isbell adjunctions and Kan adjunctions Lili Shen and Dexue Zhang 577

Enriched indexed categories Michael Shulman 616

Tight spans, Isbell completions and semi-tropical modules Simon Willerton 696

The algebra of the nerves of omega-categories Richard Steiner 733 Complicial structures in the nerves of omega-categories Richard Steiner 780

Multitensor lifting and strictly unital higher category theory Michael Batanin, Denis-Charles Cisinski and Mark Weber 804

Multitensors as monads on categories of enriched graphs Mark Weber 857

A double categorical model of weak 2-categories Simona Paoli and Dorette Pronk 933

Forms and exterior differentiation in Cartesian differential categories G.S.H. Cruttwell 981

Relative Mal’tsev categories Tomas Everaert, Julia Goedecke, Tamar Janelidze-Gray and Tim Van der Linden 1002

On theories of superalgebras of differentiable functions David Carchedi and Dmitry Roytenberg 1022

Tannaka–Krein duality for compact quantum homogeneous spaces. I. General theory Kenny De Commer and Makoto Yamashita 1099

The Gleason cover of a realizability topos Peter Johnstone 1139

Galois theories of commutative semigroups via semilattices Isabel A. Xarez and Joao J. Xarez 1153

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: robert.walters@uninsubria.it R. J. Wood, Dalhousie University: rjwood@mathstat.dal.ca