ISSN 1201-561X

[figure: T; A; C]

THEORY AND APPLICATIONS OF CATEGORIES

Volume 23, 2010

The Bourn Festscrift: A special volume dedicated to Dominique Bourn on the occasion of his 60’th birthday.

Foreword The guest editors 1

Action accessibility for categories of interest Andrea Montoli 7

Homology of n-fold groupoids Tomas Everaert and Marino Gran 22

The comprehensive factorization and torsors Ross Street and Dominic Verity 42

Snake Lemma in incomplete relative homological categories Tamar Janelidze 76

Monadic approach to Galois descent and cohomology Francis Borceux, Stefaan Caenepeel and George Janelidze 92

Internal crossed modules and Peiffer Condition Sandra Mantovani, Giuseppe Metere 113 Strongly separable morphisms in general categories G. Janelidze and W. Tholen 136

The Editors of TAC wish to thank Andree Ehresmann, George Janelidze, Jiri Rosicky, Walter Tholen and Enrico Vitale who acted as guest editors for this special volume.

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

granted.

The third cohomology group classifies double central extensions Diana Rodelo and Tim Van der Linden 150

Star-multiplicative graphs in pointed protomodular categories N. Martins-Ferreira 170

A metric tangential calculus Elisabeth Burroni and Jacques Penon 199

The pointed subobject functor, 3 x 3 lemmas, and subtractivity of spans Zurab Janelidze 221

A categorical approach to integration Reinhard Brger 243

What are sifted colimits? J. Adamek, J. Rosicky, E. M. Vitale 251

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, Cuill Inc.: valeria@cuill.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, University of Western Sydney: s.lack@uws.edu.au F. William Lawvere, State University of New York at Buffalo: wlawvere@acsu.buffalo.edu Tom Leinster, University of Glasgow, T.Leinster@maths.gla.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