ISSN 1201-561X

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THEORY AND APPLICATIONS OF CATEGORIES Volume 13, 2004

The Carboni Festschrift: A special volume dedicated to Aurelio Carboni on the occasion of his 60’th birthday.

Foreword The guest editors 1

On von Neumann varieties F. Borceux and J. Rosicky 5

Commutator theory in strongly protomodular categories Dominique Bourn 27

On extensions of lax monads Maria Manuel Clementino and Dirk Hofmann 41

Universal properties of Span R.J.MacG. Dawson, R. Paré and D.A. Pronk 61

Derivations of categorical groups A.R. Garzon, H. Inassaridze and A. del Rio 86 Semi-abelian monadic categories Marino Gran and Jiri Rosicky 106

The Editors of TAC wish to thank G. Janelidze, S. Lack, F.W. Lawvere, E.M. Vitale and R.J. Wood who acted as guest editors for this special volume.

\begin{matrix}c \\ ◯ \end{matrix} The Editors of Theory and Applications of Categories 2004. Permission to copy for private use

granted.

Normed combinatorial homology and noncommutative tori Marco Grandis 114

Coalgebras, braidings, and distributive laws Stefano Kasangian, Stephen Lack, and Enrico M. Vitale 129

Composing PROPs Stephen Lack 147

Functorial concepts of complexity for finite automata F. William Lawvere 164

Every small Sl-enriched category is Morita equivalent to an Sl-monoid Bachuki Mesablishvili 169

Split structures Robert Rosebrugh and R.J. Wood 172

The monoidal centre as a limit Ross Street 184

Generic morphisms, parametric representations and weakly cartesian monads Mark Weber 191

Internal monotone-light factorization for categories via preorders Joao Xarez 235

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.

Michael Barr, McGill University: barr@barrs.org, Associate Managing Editor Lawrence Breen, Université Paris 13: breen@math.univ-paris13.fr Ronald Brown, University of Wales Bangor: r.brown@bangor.ac.uk Jean-Luc Brylinski, Pennsylvania State University: jlb@math.psu.edu Aurelio Carboni, Università dell Insubria: aurelio.carboni@uninsubria.it Valeria de Paiva, Palo Alto Research Center: paiva@parc.xerox.com 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@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 Robert Rosebrugh, Mount Allison University: rrosebrugh@mta.ca, Managing Editor Jiri Rosicky, Masaryk University: rosicky@math.muni.cz 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