ISSN 1201-561X

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THEORY AND APPLICATIONS OF CATEGORIES

Volume 16, 2006

Monads of effective descent type and comonadicity Bachuki Mesablishvili 1

Action groupoid in protomodular categories Dominique Bourn 46

Inverting weak dihomotopy equivalence using homotopy continuous flow Philippe Gaucher 59

Frobenius algebras and ambidextrous adjunctions Aaron D. Lauda 84

Every Grothendieck topos has a one-way site Colin McLarty 123

Points of affine categories and additivity A. Carboni and G. Janelidze 127

Preserving homology Michael Barr 132

Thin fillers in the cubical nerves of omega-categories Richard Steiner 144 Free A_{∞}-categories Volodymyr Lyubashenko and Oleksandr Manzyuk 174

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granted.

A characterization of quantic quantifiers in orthomodular lattices Leopoldo Román 206

Exponentiability in lax slices of Top Susan Niefield 218

Closedness properties of internal relations I: A unified approach to Mal’tsev, unital and subtractive categories Zurab Janelidze 236

Closedness properties of internal relations II: Bourn localization Zurab Janelidze 262

Categorical structures enriched in a quantaloid: tensored and cotensored categories Isar Stubbe 283

Stable meet semilattice fibrations and free restriction categories J.R.B. Cockett and Xiuzhan Guo 307

TFT Construction of RCFT correlators V: Proof of modular invariance and factorisation Jens Fjelstad, Jurgen Fuchs, Ingo Runkel and Christoph Schweigert 342

Spectra of finitely generated Boolean flows John F. Kennison 434

Paths in double categories R. J. MacG. Dawson, R. Paré, and D. A. Pronk 460

Numerology in topoi Peter Freyd 522

Categorical representations of categorical groups John W. Barrett and Marco Mackaay 529

Compactifications, C(X) and ring epimorphisms W.D. Burgess and R. Raphael 558 On categorical crossed modules P. Carrasco, A.R. Garzon and E.M. Vitale 585

Equivalence of 2D-multitopic category and ana-bicategory Param Jyothi Reddy R 619

Descent for Monads Pieter Hofstra and Federico De Marchi 668

Topological *-autonomous categories Michael Barr 700

Quotient models of a category up to directed homotopy Marco Grandis 709

Categories of components and loop-free categories Emmanuel Haucourt 736

Pullback and finite coproduct preserving functors between categories of permutation representations Elango Panchadcharam and Ross Street 771

Categorified algebra and quantum mechanics Jeffrey Morton 785

A cohomological description of connections and curvature over posets John E. Roberts and Giuseppe Ruzzi 855

Generating families in a topos Toby Kenney 896

Copower objects and their applications to finiteness in topoi Toby Kenney 943

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.

Managing editor. Robert Rosebrugh, Mount Allison University: rrosebrugh@mta.ca

TEXnical editor. Michael Barr, McGill University: mbarr@barrs.org

Transmitting editors.

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: r.brown@bangor.ac.uk Aurelio Carboni, Università dell Insubria: aurelio.carboni@uninsubria.it Valeria de Paiva, Xerox Palo Alto Research Center: paiva@parc.xerox.com

Ezra Getzler, Northwestern University: getzler(at)math(dot)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 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@acsu.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 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