ISSN 1201-561X

[figure: T; A; C]

THEORY AND APPLICATIONS OF CATEGORIES

Volume 27, 2012-13 A special volume of articles from the CT2011 conference.

Introduction The guest editors 1

Remarks on exactness notions pertaining to pushouts Richard Garner 2

Exponentiability via double categories Susan Niefield 10

On the axioms for adhesive and quasiadhesive categories Richard Garner and Stephen Lack 27

The core of adjoint functors Ross Street 47

Weakly Mal’tsev categories and strong relations Zurab Janelidze and Nelson Martins-Ferreira 65

Symmetry of regular diamonds, the Goursat property, and subtractivity Marino Gran, Zurab Janelidze, Diana Rodelo and Aldo Ursini 80

Exact completions and small sheaves Michael Shulman 97 The Ursini commutator as normalized Smith-Pedicchio commutator Sandra Mantovani 174

The Editors of TAC wish to thank Marino Gran, George Janelidze, Stephen Lack, John MacDonald and Walter Tholen who acted as guest editors for this special volume.

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

granted.

Higher central extensions via commutators Diana Rodelo and Tim Van der Linden 189

Descent in monoidal categories Bachuki Mesablishvili 210

The *-autonomous category of uniform sup semi-lattices Michael Barr, John F. Kennison, and R. Raphael 222

Lawvere completeness as a topological property Serdar Sozubek 242

Generalized Hopf modules for bimonads Marcelo Aguiar and Stephen U. Chase 263

Proper maps for lax algebras and the Kuratowski-Mrówka theorem Maria Manuel Clementino and Walter Tholen 327

On actions and strict actions in homological categories Manfred Hartl and Bruno Loiseau 347

Composition of modules for lax functors Robert Paré 393

Elementary quotient completion Maria Emilia Maietti and Giuseppe Rosolini 445

An equational metalogic for monadic equational systems Marcelo Fiore 464

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