January 1996 - Categories - categories.org.au

groupoids
by Alan Weinstein 31 Jan '96

31 Jan '96

Dear Colleagues, I've just finished a survey article entitled "Groupoids: unifying internal and external symmetry", which I have submitted to the Notices of the AMS. It is available as a postscript file via email (alanw(a)math.berkeley.edu) or my web page (http://math.berkeley.edu/~alanw) Comments are welcome, of course. Alan Weinstein

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TSM - Second Announcement
by York cat 30 Jan '96

30 Jan '96

TORONTO SPRING MEETING A Weekend Meeting on Category Theory and Its Applications YORK UNIVERSITY, North York (Metropolitan Toronto) Saturday/Sunday, April 13/14, 1996 Second Announcement Principal Speakers: Andre JOYAL, Universite de Quebec a Montreal Robert PARE, Dalhousie University, Halifax Cristina PEDICCHIO, Universita di Trieste Registration: There is a registration form attached to this message. If you intend to attend the meeting, please fill it out as soon as possible and return it to yorkcat(a)mathstat.yorku.ca There will be a registration fee, payable upon arrival, of $25 per employed participant ($12 for others) to cover expenses for refreshments and a common lunch on Saturday. Contributed talks: There will be morning and afternoon sessions for contributed talks on April 13 (starting at 9 a.m.) and a morning session on April 14 (ending by 2 p.m.). Talks will be a maximum of 30 minutes each. Anyone who is interested in speaking at the meeting should indicate this on the registration form. If there are more potential speakers than time slots, the organizers will endeavour to follow the policy of first-come-first-served. Location of meeting: The meeting will take place on the main campus of York University, 4700 Keele St, North York, which is in the northwestern area of Metropolitan Toronto. Highway 401 is the best major highway for accessing the campus by car. There is an exit for Keele St off 401; York University is approximately 4-5 miles north of 401, north of Finch Avenue. There are traffic lights and a large sign at the main entrance of the University, which is on the left-hand (west) side of Keele. Specificc directions about reaching the university from various accommodations are given below. Detailed information concerning the venue of the conference will be given in the Third Announcement. Maps will be installed on the WWW (see below); hardcopies can be mailed to participants upon request. Travel: Having a car in Toronto would be an advantage and would maximize enjoyment of the weekend. However, public transportation is good, and we shall suggest a number of hotels from which the Univeristy is easily accessed. Pearson International Airport is not far from the University. Taxi fare to the University or environs is approximately $25-30. Taxi fare to downtown hotels is approximately $30-40. There is also a bus connection with the downtown hotels and with the Yorkdale Shopping Centre, which also has a subway stop; for further information, see below. Participants from Montreal can also book flights which arrive at the downtown Island Airport. Union Station, the train terminal, is located downtown across from the Royal York Hotel and not far from the other downtown hotels. The bus terminal is also located conveniently downtown. Accommodations: We have reserved a small contingent of guest rooms in the student dormitories ($25 per night) which will be given with preference to graduate students. In general we recommend that participants reserve rooms in one of the North York or downtown hotels listed below. All hotels with the exception of the Holiday Inn Express (details below) should be called directly. Your choice of accommodation should be guided by cost and additional planned activities during your stay. Hotels near the campus will shorten transportation time to the meeting, but they are generally not in scenic areas. We point out that for those who can extend their stay or arrive early on Friday, Toronto offers a wide selection of museums, live theatre, and musical or sporting events, as well as excellent shopping and restaurants. To take full advantage of these activities, a downtown hotel or hotel near the subway line is recommended. Saturday night: In view of the length of the meeting and the scope of activities in Toronto, we have decided to forego a saturday evening party. We will have information on recommended restaurants at the meeting and will circulate some information on cultural events with the Third Announcement. Welcome reception on Friday night: Participants are invited to an informal welcome party on friday night with wine and cheese in Walter Tholen's home beginning from 8 p.m. Directions will be given in the Third Announcement. Information on the web: Up-dated information on the TSM can be obtained on Walter Tholen's home page on the World Wide Web: htpp://www.math.yorku.ca/Who/Faculty/Tholen/menu.html Please see below for information on hotels, public transport, airport buses, and for the registration form. The Third Announcement will be circulated before April 1. We hope to see you in Toronto in April! Xiaomin Dong Sandro Fusco Joan Wick Pelletier Walter Tholen ******************************************************************************** Hotel list: This list is divided in two groups, North York and Downtown. The hotels in North York will allow for a shorter commuting distance to the university than the downtown hotels. They are comfortable and reasonably priced. However, with the exception of Novotel, they are located in industrial or commercial areas of the city and, hence, do not offer attractive scenery. The downtown hotels provide a generally attractive city ambience, but they may pose a Sunday morning transportation problem for participants without cars, since the subway does not run before 9 a.m. on Sunday. Thus, those who stay downtown must be prepared to take a taxi or a sequence of buses that morning. N O R T H Y O R K - Montecassino Place Hotel 3710 Chesswood Dr. (@ Sheppard) Tel. (416) 630-8100 Executive Queen Room: $58.04 Executive Double Room: $58.04 Remarks: - mention York U. (ask for Rosita DelGrande) when booking - complimentary continental breakfast, free outdoor parking - close to the subway line leading to downtown (take 106 or 108 bus eastbound, 5 mins) - if arriving by car, exit highway 401 at Allen Road and go north and then west on Sheppard - to reach the university by public transport, take the 106 bus westbound to York U (10 mins) - Howard Johnson Keele St & Hwy 401 Tel.(416) 636-4656 Single Room: $75 (+$10 for breakfast) Double Room: $85 (______"___________) Remarks: - mention York U when booking - free parking (outdoor or covered parkette) - if arriving by car, exit highway 401 at Keele Street and go north - to reach the university by public transport, take any Keele bus north to York U (get off at the main gate of the Universty, 10 min. walk to conference building) - Ramada Hotel 400-401 1677 Wilson Ave. (Jane & Wilson) Tel. (416) 249-8171 Single Room: $65 Double Room: $65 (+ $10 for each additional person) Remarks: - mention York University block of rooms when booking - free outdoor parking - shuttle service from and to the airport (one way fare: $5/person) - if arriving by car, exit highway 401 at Black Creek Drive/Jane Street, take Jane Street north and then go west on Wilson - to reach the university by public transport, take the Wilson bus (96 bus) east to Keele, then any Keele bus north to York U (get off at the main gate) - Holiday Inn @ Yorkdale Hwy 401 & Dufferin Tel. (416) 789-5161 Single Room: $93 Double Room: $93 Remarks: - mention Cat Theory TSM when booking - free outdoor parking - walking distance from subway line, and from Yorkdale Shopping Mall (2nd largest shopping mall in Toronto) - if arriving by car: * FROM Westbound Hwy 401: Exit Allen Rd., take Yorkdale Rd N. Follow along north side of Yorkdale Mall. At lights, cross over Dufferin St. to Bridgeland Ave.; hotel entrance is on south side, turn left to driveway. * FROM Eastbound Hwy 401: Exit Dufferin St. South. Turn right into Plaza Pontiac dealership; stay to right to enter hotel parking lot. - to reach the university by public transport, take the subway north to Wilson Stn. (one stop north), then the 106 bus to York U. (25 mins) - Novotel 3 ParkHome (3 lights north of Sheppard & Yonge) Tel. (416) 733-2929 Single Room: $89 Double Room: $89 Remarks: - ask for corporate rates for York U. - parking available for $8.25/day (IN/OUT privileges) - if arriving by car, exit highway 401 at Yonge Street and go north - to reach the university by public transport, take the subway to the Sheppard station or, on Sunday morning before 9 a.m.,any Yonge bus south to Sheppard subway stn., then the 84 bus west to Sentinel Rd, and FINALLY take the 106 bus north to York U - easy connection to downtown by subway (or by bus throughout the night), indoor walk to subway station - Holiday Inn Express 30 Norfinch Drive (@ Finch Ave) Tel. (416) 665-3500 Single Room: $46 Double Room: $46 Remarks: - to obtain the indicated rates, reservation must be done through yorkcat(a)mathstat.yorku.ca (see Registration Form below) - complimentary continental breakfast, free parking - if arriving by car, exit highway 400 at Finch Ave, go one block east - to reach the university by public transport, take the Finch bus (36 or 118) east to Sentinel Rd., then the 106 bus north to York U D O W N T O W N Note: all downtown hotels are within walking distance to the subway. - Days Inn Hotel 30 Carlton St (@ Yonge St) Tel. (416) 977-6655 Single Room: $59 Double Room: $59 (+ $5 for each additional person) Remarks: - mention Cat Theory TSM at York U when booking - indoor parking available for $11.50/day (IN/OUT privileges) - to reach the conference site by public transport, take the subway to Wilson Stn., then 106 bus to York U (stops on campus) , OR take the subway to Finch Stn., then the 60C or 60F bus to York U (stops off campus) - Town Inn Hotel 620 Church St (south of Bloor St) Tel. (416) 964-3311 North East USA call toll free: 1-800-387-2755 Single Suite (w kitchen): $75 Double Suite (w kitchen): $85 Remarks: - mention York U. Math Conference (ask for Cora) when booking - free continental breakfast - indoor parking available for $13/day (IN/OUT privileges) - to reach the conference site by public transport, see remarks for Days Inn Hotel - Delta Chelsea Inn 33 Gerrard St. West (@ Yonge St) Tel. (416) 595-1975 Single Room: $81 Double Room: $96 Remarks: - ask for corporate rates for York U when booking - underground parking available for $16/day (IN/OUT privileges) - to reach the conference site by public transport, see remarks for Days Inn Hotel - Royal York Hotel 100 Front St. West Tel. (416) 863-6333 Single Room: $121 Double Room: $121 (+ $20 for each additional person) Remarks: - ask for corporate rates for York U when booking - indoor parking available for $10/24 hrs + $4.50 for IN/OUT privileges - to reach the conference site by public transport, take the subway to Wilson Stn., then 106 bus to York U. Directions on how to reach the downtown area by car: - From Buffalo and Niagara Falls: Queen Elisabeth Way into Gardiner Expressway. Exit at Yonge Street, and go north. - From Detroit, Windsor or Montreal: Hwy 401 to Yonge Street, then go south. ******************************************************************************** Times of operation of public transport: SATURDAY First subway train from Union Stn.: 6:04am Last subway train from Union Stn.: 1:15am First 106 bus from Wilson Stn.: 6:00am (every 15 mins) Last 106 bus from Wilson Stn.: 2:15am First Keele bus from Hwy 401 going north: 5:12am SUNDAY First subway train from Union Stn.: 9:16am First 106 bus from Wilson Stn.: 7:45am (every 30 mins) Last 106 bus from Wilson Stn.: 1:15am First Keele bus from Hwy 401 going north: 6:58am ******************************************************************************** Information about Airport Express shuttles (a) International Airport <--> Yorkdale Shopping Mall Buses leave every 40 mins. First bus at 5:00am Ride is approximately 25 mins Fare: - one-way ticket $ 6.90 - return ticket $11.95 (valid for 1 year). (b) International Airport <--> Downtown Buses leave every 20 mins. First bus at 5:00am Ride is approximately 40 mins Fare: - one-way ticket $11.45 - return ticket $19.70 (valid for 1 year). The bus stops at Royal York Hotel, and Delta Chelsea Inn. From there, take the north connector (at no extra charge) for the other downtown hotels. ********************************* CUT HERE ************************************ Registration Form - Toronto Spring Meeting (To be returned to yorkcat(a)mathstat.yorku.ca at your earliest convenience) Name: I intend to attend the meeting: Yes/No I intend to give a talk: Yes/No/Do not know yet Title: (desired length 20/30 min.) Only if applicable, fill out the following: I would like to reserve - a room in a student dormitory from (arrival date) to (departure date) - a (single/double) room in the Holiday Inn Express from (arrival date) to (departure date) Please note: For bookings on campus or in the Holiday Inn Express prepayment will be reqired. Once we have received your registration, you will be contacted concerning payment.

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correction to `From ... resolution'
by James Otto 27 Jan '96

27 Jan '96

Dear People, A correction was made to the 1-23-96 version of ftp://triples.math.mcgill.ca/pub/otto/res Regards, Jim 1-27-96

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PhD Scholarships at Chalmers, Gothenburg
by Henrik Persson 26 Jan '96

26 Jan '96

My sincere apologies if you receive this more than once. Please feel free to circulate it to others who may be interested. Best regards, Henrik ----------------------------------------------------------------------- The Department of Computing Science at the Chalmers University of Technology and G\"{o}teborgs University announces free PhD positions. The Department of Computing Science has about 30 staff members and about 25 PhD students. The department receives funding from Esprit, and from the Swedish Government agencies TFR and NUTEK. The major topics of research are programming logic and type theory, functional programming and concurrency, but research is also carried out in a number of other topics. Most PhD positions are five year scholarships. The PhD student will spend about 80 percent of his or her time on graduate studies, and about 20 percent on teaching. Applicants must have an undergraduate degree in Computer Science with excellent results. The department tries to increase the number of female employees, and especially welcomes female applicants. At the moment the scholarships consist of 14000 (17200) SEK per month in the first (last) year. More information about the graduate programmes can be found on the WWW on page: http://www.cs.chalmers.se/ComputingScience/Graduate To apply, send us a letter in English, covering 1 data about yourself; 2 a copy of an official paper giving grades from your undergraduate degree(s); 3 a statement about your main interests; 4 some letters of recommendation from people that know you as a student or as an employee; 5 any scientific papers you have written. Send your application to Section for Mathematics and Computer Science Chalmers University of Technology 412 96 Gothenburg Sweden Furthermore, send an email containing the data about yourself to johanj(a)cs.chalmers.se The last date for your application to arrive is March 1, 1996. A decision about to whom we will offer the PhD positions will be taken before June 1, 1996.

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More on Mike Barr's question
by Ross Street 24 Jan '96

24 Jan '96

There has been some further discussion between Mike Barr and me on modules between monoids in a complete, cocomplete, closed monoidal category. Mike responded: >If I have understood your theorem, it is claimed only for the case that >the original category is braided. I was interested in the genuinely >asymmetric case, so this doesn't apply. Although your arguments >are probably valid in that case, at a guess. Have I missed something? So I said: It looks as though **I** missed something. I didn't include the older fact well known to enriched category theorists: even without any symmetry or braiding, V-Mod is a bicategory in which all right extensions and right liftings exist (I don't like the word "biclosed"; I use "left closed", "right closed" and "closed" for both when dealing with a monoidal category). In particular, for any V-category A, each hom category V-Mod(A,A) is a closed monoidal category under composition (= tensor product) of modules (as before, I don't say "bimodules" either). Even more particularly you can take A to be a monoid in V. For this there ARE references. I believe Benabou, in his Louvain-la-neuve notes "Les Distributeurs" Rapport No 33 jan 1973, only looked at the case of V symmetric. Same is true of Bill Lawvere's "Metric spaces" paper. But it is not hard to generalise. My paper Enriched categories and cohomology, Quaestiones Math. 6 (1983) 265-283; MR85e:18007 does the non-symmetric case. But it does it more generally for V a bicategory (without commutativity you might as well have "several objects"). Other papers which build on this are: Cauchy characterization of enriched categories, Rendiconti del Seminario Matematico e Fisico di Milano 51 (1981) 217-233; MR85e:18006. (with R. Betti, A. Carboni, and R. Walters) Variation through enrichment, J. Pure Appl. Algebra 29 (1983) 109-127; MR85e:18005. (with A. Carboni, S. Johnson and D. Verity) Modulated bicategories, J. Pure Appl. Algebra 94 (1994) 229-282. Gordon and Power have also done Gabriel-Ulmer duality for W-Mod where W is a decent bicategory (homs locally presentable). JPAA? The recent thing with Brian Day looks at when V-Mod itself is "monoidal", a natural step beyond the above references & studied by Carboni, Walters et al in the case where V is a poset (or W is locally a poset). Best wishes, Ross

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Bangor WWW Pages
by Prof R. Brown 24 Jan '96

24 Jan '96

We now have some material available on the world wide web for downloading as postscript files. The School of Mathematics, University of Wales, Bangor may be accessed at http://www.bangor.ac.uk/ma/ The following papers are available as postcript files via R. Brown's home page http://www.bangor.ac.uk/~mas010/home.html R. Brown and W. Dreckmann, ``Domains of data and domains of terms in AXIOM''. Abstract: This gives a general account and the source Axiom 2.0 code for directed graphs, free categories, free groupoids, which will give an impression of coding in Axiom. R. Brown and O. Mucuk, ``The monodromy groupoid of a Lie groupoid'', {\em Cah. Top. G\'eom. Diff. Cat}, 36 (1995) 345-369. Abstract: We show that under general circumstances, the disjoint union of the universal covers of the stars of a Lie groupoid admits the structure of a Lie groupoid, such that the projection has a monodromy property on the extension of local smooth morphisms. This completes a detailed account of results announced by J Pradines. R. Brown and O. Mucuk, ``Foliations, locally Lie groupoids, and holonomy'', {\em Cah. Top. G\'eom. Diff. Cat}, (1996) (to appear). Abstract: We show that a paracompact foliated manifold determines a locally Lie groupoid (or piece of a differentiable groupoid, in the sense of Pradines). This allows for the construction of holonomy and monodromy groupoids of a foliation to be seen as particular cases of constructions for locally Lie groupoids. R. Brown, ``Representation and computation for crossed modules'', Proceedings {\em Cat\'egories, Algebres, Esquisses, Neo-esquisses}, Caen, 1994, 6pp. Abstract: We argue for the need to develop `structural computation', to handle the translation of algebraic structures between equivalent categories. This is illustrated with the problem of the tensor product in the equivalent categories of crossed modules over groupoids, double groupoids with connection, 2-groupoids. R. Brown, M. Golasinski, T.Porter, and A.P.Tonks, ``On function spaces of equivariant maps and the equivariant homotopy theory of crossed complexes.'' 18pp Abstract: This paper gives an equivariant version of the homotopy theory of crossed complexes for the case of a discrete group action. The applications generalise work on equivariant Ellenberg-MacLane spaces, including the non-abelian case of dimension 1, and on local systems. It also generalises the theory of equivariant 2-types, due to Moerdijk and Svensson. Further we give results not just on the homotopy classification of maps, but also on the homotopy types of certain equivariant function spaces. (Indag. Math. (to appear)) R. Brown and T. Porter, ``On the Schreier theory of non-abelian extensions: generalisations and computations'', 21pp Abstract: Classically, a Schreier 2-cocycle for a group G involves functions on the 3-fold and 2-fold products of G with itself. We show how a crossed resolution may be used to give smaller and more computable presentations of such cocycles, which are determined by a presentation of G and identities among relations. This is a modern expression of ideas of Turing, 1938. R. Brown and C.D.Wensley, ``Computing crossed modules induced by an inclusion of a normal subgroup, with applications to homotopy 2-types'', 9pp Abstract: We suppose M, P are normal subgroups of a group Q and prove directly a value for the crossed Q-module induced from the crossed P-module M by the inclusion of P in Q. Using methods of free crossed resolutions, we calculate explicitly the k-invariant of this induced crossed module, in the case when Q/P is finite cyclic. We also use coproducts of crossed P-modules to obtain some general results on induced crossed modules, again when P is normal in Q. These results are applied to the 2-type of homotopy pushouts of certain maps of classifying spaces of discrete groups. This continues work of a previous paper, published in TAC, 1995, no.3. R. Brown and G. Janelidze, ``Van Kampen theorems for categories of covering morphisms in lextensive categories'', 9pp, (J. Pure Applied Algebra, to appear). Abstract: We show that lextensive categories are a natural setting for statements and proofs of the ``tautologous'' Van Kampen theorem, in terms of coverings of a space. R. Brown and G. Janelidze, ``Galois theory of second order covering maps of simplicial sets'', 10pp, submitted, 1995. Abstract: We give a version for simplicial sets of a second order notion of covering map, which bears the same relation to the usual coverings as do groupoids to sets. The Generalised Galois theory of the second author yields a classification of such coverings by the action of a certain kind of double groupoid. The following papers are available as postcript files via T. Porter's home page http://www.bangor.ac.uk/~mas013/home.html Bangor Maths Preprint No. 95.08 Spaces of maps into classifying spaces for equivariant crossed complexes. Authors: R. Brown, M. Golasinski, T. Porter, and A. Tonks September 13, 1995 (see above) Keywords: Equivariant homotopy, crossed complexes AMS Subject Classification: 55P91, 55U10, 55U35 Bangor Maths Preprint No.95.09 Title: Categorical Aspects of Equivariant Homotopy Authors:.-M. Cordier and T. Porter Date: September 13, 1995 Abstract: Using the theory of homotopy coherent Kan extensions, results of Elmendorf and Dwyer and Kan are generalised. This produces simplicially enriched equivariant versions of the singular complex / geometric realisation adjunction of the non- equivariant theory. Keywords: Homotopy coherent Kan extension, simplicially enriched categories, G-equivariant homotopy AMS Subject Classification: 55P91, 18G55, 18D20, 18G30 Type of file: LATEX or dvi No. of pages: 18 Bangor Maths Preprint No. 95.10 Title: Homotopy coherent category theory Authors: J.-M. Cordier and T Porter Abstract: This article is an introduction to the categorical theory of homotopy coherence. It is based on the construction of the homotopy coherent analogues of end and coend, extending ideas of Meyer and others. The paper aims to develop homotopy coherent analogues of many of the results of elementary category theory, in particular it handles a homotopy coherent form of the Yoneda lemma and of Kan extensions. This latter area is linked with the theory of generalised derived functors. Keywords: Simplicially enriched categories, Homotopy coherent ends and coends, Yoneda lemma AMS Subject Classification: 18D20, 18D05, 18G30, 18A99 Type of file: dvi, or Postscript No. of pages: 54 Bangor Maths Preprint No. 95.11 Title: Interpretations of Yetter's notion of G-coloring: simplicial fibre bundles and non-abelian cohomology Authors: T Porter Date: October 11, 1995 Abstract: This paper notes and explores the connection between Yetter's notion of G-coloring where G is either a finite group or a finite `Categorical group' and the theory of simplicial fibre bundles. This allows an interpretation of Yetter's topological quantum field theory in terms of equivalence classes of simplicial fibre bundles. If G is a finite categorical group, these fibre bundles have interesting lifting properties and their fibres are groupoids. Using recent results and descriptions of non-abelian cohomology due to Breen and Duskin, these fibre bundles are linked with non-abelian cocycles with coefficients in G. Keywords: Topological Quantum Field Theory, fibre bundle, non- abelian cohomology AMS Subject Classification: 81T99, 57N70, 55R99 Type of file: Postscript or dvi. No. of pages: 30 Prof R. Brown School of Mathematics Dean St University of Wales Bangor Gwynedd LL57 1UT UK Tel: (direct) +44 1248 382474 (office) +44 1248 382475 Fax: +44 1248 355881 email: mas010(a)bangor.ac.uk wwweb: http://www.bangor.ac.uk/~mas010/home.html wwweb for maths: http: //www.bangor.ac.uk/ma

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draft paper: From Horn formula to Makkai sketch resolution
by categories 24 Jan '96

24 Jan '96

Date: Mon, 22 Jan 1996 23:42:51 -0500 From: James Otto <otto(a)triples.math.mcgill.ca> Dear People, The plain text draft paper, whose title and abstract follows, is availabe by web or ftp at ftp://triples.math.mcgill.ca/pub/otto/res and is linked to ftp://triples.math.mcgill.ca/pub/otto/otto.html Best regards, Jim From Horn formula to Makkai sketch resolution J. Otto January 22, 1996 otto(a)triples.math.mcgill.ca Abstract. We provide a basis for logic programming into locally finitely presentable (or l.f.p.) categories. We thus begin to consider higher order logic programming. Horn formulas, in particular systems of equations, generalize to finite Makkai (or M-) sketches. Further, models of sets of Horn clauses generalize to, again called models and forming the l.f.p. categories, M-sketches orthogonal to sets of maps (axioms) between finite M-sketches. Resolutions compute maps (answers) from finite M-sketches (queries) to initial models. Resolutions are cospans and lift to compositions of special resolutions.

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Theory and Applications of Categories: Abstracts, Volume 1
by Bob Rosebrugh 19 Jan '96

19 Jan '96

The table of contents and abstracts for Volume 1 (1995) of Theory and Applications of Categories follows. Access via the WWW is at http://www.tac.mta.ca/tac/ For subscriptions write to tac(a)mta.ca ---------------------------------------------------------------------- ISSN 1201-561X THEORY AND APPLICATIONS OF CATEGORIES Volume 1, 1995 Oriented singular homology Michael Barr 1 Functorial and algebraic properties of Brown's P functor Luis-Javier Hern\'andez-Paricio 10 On finite induced crossed modules, and the homotopy 2-type of mapping cones Ronald Brown and Christopher D. Wensley 54 Kan extensions along promonoidal functors Brian Day and Ross Street 72 Symmetric monoidal categories model all connective spectra R. W. Thomason 78 Distributive adjoint strings Robert Rosebrugh and R. J. Wood 119 A forbidden-suborder characterization binarily-composable diagrams in double categories Robert Dawson 146 Categorical data-specifications Frank Piessens and Eric Steegmans 156 On the size of categories Peter Freyd and Ross Street 174 -------------------------------------------------------------------- Oriented Singular Homology Michael Barr We formulate three slightly different notions of oriented singular chain complexes and show that all three are naturally homotopic to ordinary singular chain complexes. Theory and Applications of Categories, Vol 1, No. 1, 1-9. ftp://ftp.tac.mta.ca/pub/tac/html/volumes/1995/n1/v1n1.{dvi,ps} --------------------------------------------------------------------- Functorial and algebraic properties of Browns P functor Luis-Javier Hernandez-Paricio In 1975 E. M. Brown constructed a functor $\cal P$ which carries the tower of fundamental groups of the end of a (nice) space to the Brown-Grossman fundamental group. In this work, we study this functor and its extensions and analogues defined for pro-sets, pro-pointed sets, pro-groups and pro-abelian groups. The new versions of the $\cal P$ functor are provided with more algebraic structure. Examples given in the paper prove that in general the $\cal P$ functors are not faithful, however, one of our main results establishes that the restrictions of the corresponding $\cal P$ functors to the full subcategories of towers are faithful. We also prove that the restrictions of the $\cal P$ functors to the corresponding full subcategories of finitely generated towers are also full. Consequently, in these cases, the towers of objects in the categories of sets, pointed sets, groups and abelian groups, can be replaced by adequate algebraic models ($M$-sets, $M$-pointed sets, near-modules and modules.) The article also contains the construction of left adjoints for the $\cal P$ functors. Theory and Applications of Categories, Vol. 1, No. 2, 10-53 ftp://ftp.tac.mta.ca/pub/tac/html/volumes/1995/n2/v1n2.{dvi,ps} ----------------------------------------------------------------------- On finite induced crossed modules and the homotopy 2-type of mapping cones, Ronald Brown and Christopher D. Wensley Results on the finiteness of induced crossed modules are proved both algebraically and topologically. Using the Van Kampen type theorem for the fundamental crossed module, applications are given to the 2-types of mapping cones of classifying spaces of groups. Calculations of the cohomology classes of some finite crossed modules are given, using crossed complex methods. Theory and Applications of Categories, Vol. 1, No. 3, 54-71 ftp://ftp.tac.mta.ca/pub/tac/html/volumes/1995/n3/v1n3.{dvi,ps} ------------------------------------------------------------------------ Kan extensions along promonoidal functors Brian Day and Ross Street Strong promonoidal functors are defined. Left Kan extension (also called "existential quantification") along a strong promonoidal functor is shown to be a strong monoidal functor. A construction for the free monoidal category on a promonoidal category is provided. A Fourier-like transform of presheaves is defined and shown to take convolution product to cartesian product. Theory and Applications of Categories, Vol. 1, No. 4, 72-78 ftp://ftp.tac.mta.ca/pub/tac/html/volumes/1995/n4/v1n4.{dvi,ps} -------------------------------------------------------------------------- Symmetric monoidal categories model all connective spectra R. W. Thomason The classical infinite loopspace machines in fact induce an equivalence of categories between a localization of the category of symmetric monoidal categories and the stable homotopy category of -1-connective spectra. Theory and Applications of Categories, Vol. 1, No. 4, 79-118 ftp://ftp.tac.mta.ca/pub/tac/html/volumes/1995/n5/v1n5.{dvi,ps} -------------------------------------------------------------------------- Distributive Adjoint Strings R. Rosebrugh and R. J. Wood For an adjoint string V -| W -| X -| Y : B --> C, with Y fully faithful, it is frequently, but not always, the case that the composite VY underlies an idempotent monad. When it does, we call the string distributive. We also study shorter and longer `distributive' adjoint strings and how to generate them. These provide a new construction of the simplicial 2-category, Delta. Theory and Applications of Categories, Vol. 1, No. 6, 119-145 ftp://ftp.tac.mta.ca/pub/tac/html/volumes/1995/n6/v1n6.{dvi,ps} -------------------------------------------------------------------------- A forbidden-suborder characterization of binarily-composable diagrams in double categories, Robert Dawson Tilings of rectangles with rectangles, and tileorders (the associated double order structures) are useful as ``templates'' for composition in double categories. In this context, it is particularly relevant to ask which tilings may be joined together, two rectangles at a time, to form one large rectangle. We characterize such tilings via forbidden suborders, in a manner analogous to Kuratowski's characterization of planar graphs. Theory and Applications of Categories, Vol. 1, No. 7, 146-155 ftp://ftp.tac.mta.ca/pub/tac/html/volumes/1995/n7/v1n7.{dvi,ps} --------------------------------------------------------------------------- Categorical Data-Specifications F. Piessens and E. Steegmans We introduce MD-sketches, which are a particular kind of Finite Sum sketches. Two interesting results about MD-sketches are proved. First, we show that, given two MD-sketches, it is algorithmically decidable whether their model categories are equivalent. Next we show that data-specifications, as used in database-design and software engineering, can be translated to MD-sketches. As a corollary, we obtain that equivalence of data-specifications is decidable. Theory and Applications of Categories, Vol. 1, No. 8, 156-173 ftp://ftp.tac.mta.ca/pub/tac/html/volumes/1995/n8/v1n8.{dvi,ps} --------------------------------------------------------------------------- On the Size of Categories Peter Freyd and Ross Street The purpose is to give a simple proof that a category is equivalent to a small category if and only if both it and its presheaf category are locally small. Theory and Applications of Categories, Vol. 1, 1995, No. 9, 174-178 ftp://ftp.tac.mta.ca/pub/tac/html/volumes/1995/n9/v1n9.{dvi,ps}

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Freydschrift -- change of editor
by Dr. P.T. Johnstone 18 Jan '96

18 Jan '96

As previously announced on this mailing list, there will be a special issue of the Journal of Pure and Applied Algebra to mark Peter Freyd's 60th birthday. Formally, this issue is the proceedings of the Peripatetic Seminar meeting held in Edinburgh last October, which was also a celebration of Peter's birthday; but contributions are invited from any of Peter's friends who were unable to get to the Edinburgh meeting, as well. The closing date for submissions is 5 February 1996 (Peter's birthday). Originally, John Power was to have been Guest Editor for this special issue. Sadly, John has been unwell recently and has been advised to rest, so he will not be able to undertake this work, and I have agreed to take it over. The purpose of this message is therefore to ask people who are planning to submit papers for the special issue to send them not to John but to me at DPMMS, 16 Mill Lane, Cambridge CB2 1SB, U.K. If you have already sent off a paper to John, it will probably get forwarded to me; but it's advisable to send another copy direct to me, to be on the safe side. The deadline remains 5 February; it is particularly important that this date should be adhered to, since I am due to leave for a 6-week visit to Australia shortly afterwards, and any paper that fails to reach me in time to be sent off to a referee before I go will not be considered. Peter Johnstone

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bimodules in a biclosed category
by Michael Barr 17 Jan '96

17 Jan '96

Has anyone proved that if you take an "algebra" (actually monoid) object in a monoidal biclosed category that has equalizers and coequalizers, then the category of two-sided modules for that algebra is again a monoidal biclosed category. Mac Lane did this in 1965 when everything is symmetric (the tensor, the algebra and the modules) under the (surely irrelevant) assumption that the original category is also abelian. The fact is certainly true, but writing down the proof would be rather painful. Michael Barr

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