April 1992 - Categories - categories.org.au

Alan Day Conference
by bill＠kahuna.math.hawaii.edu 29 Apr '92

29 Apr '92

What follows is the second attempt at the electronic form of the second mailing for the Day Conference. Several people who should have gotten the first attempt did not. Please reply and let me know that you got this attempt. We would like to get some idea of what is going on. thanks aloha, Bill Lampe ----------------------------+------------------------------------------------- William Lampe | INTERNET: bill(a)kahuna.math.hawaii.edu Department of Mathematics | BITNET: william(a)uhunix.bitnet University of Hawaii | 2565 The Mall | Phone: (808) 956-8759 Honolulu, Hawaii 96822 | Fax: (808) 956-4659 ----------------------------+------------------------------------------------- THE ALAN DAY CONFERENCE This is the electronic version of the second mailing for the Alan Day Conference. The paper version will be mailed out in a few days. On November 26, 1990, Professor Alan Day of Lakehead University, Thunder Bay, Canada passed away. To honour his memory, a conference will be held at McMaster University, Hamilton, Ontario, Canada from 17--21 August, 1992. This conference will bring together mathematicians involved in the study of lattice theory, universal algebra, and related fields. Featured at the conference will be several talks on Alan's important contributions to lattice theory and universal algebra. We anticipate that many of the world's leading mathematicians in these areas will participate. We hope that you will be able to take part in the Alan Day Conference. Because only a limited number of people can be accommodated at McMaster, we urge you to return the enclosed forms along with your fees as early as possible. The program for the conference will begin at 9 a.m. on Monday, August 17, and finish late in the afternoon on Friday, August 21. There will be invited addresses on a variety of topics, both research and expository, and sessions of contributed talks. Participants are invited to share their research with the conference via a talk or poster display. Contributed talks should be limited to twenty minutes in order to allow time for questions and discussion. If you wish to contribute a talk, please supply the Program Committee with your name, a title, and a short abstract by July 15. This can be done by either (a) mailing the enclosed abstract form with your registration to McMaster, or (b) sending the information via email to: alan_program(a)kahuna.math.hawaii.edu (or day_prog(a)kahuna.math.hawaii.edu if your mailer can't handle names as long as alan_program.) Sending your abstract both on paper and by e-mail is the most helpful. The invited speakers include Stan Burris, Ralph Freese, Robert Goldblatt, Richard Greechie, Mark Haiman, Christian Herrmann, Jaroslav Jezek, Emil Kiss, George McNulty, J. B. Nation, Peter P. Palfy, Doug Pickering, and Steve Tschantz. Questions regarding the program may be sent to the above email addresses, or to the Program Committee in care of Prof. J. B. Nation, Department of Mathematics, University of Hawaii, Honolulu, HI 96822, USA. Algebra Universalis is planning a special issue in honour of the memory of Alan Day. This issue will also serve as conference proceedings, and all contributions will be refereed as usual. The editor for this special issue is Jiri Sichler. He requests submission of manuscripts by the start of the conference with a deadline of November 1, 1992. Papers should be submitted in the usual way to Algebra Universalis with a note indicating they are for the special issue. In addition, a copy of the TeX file for the paper (if such exists) would be useful. Send your TeX files to Sichler(a)ccm.UManitoba.CA All talks will take place in Burke Science Building or Hamilton Hall on the campus of McMaster University. In what follows, all dollar amounts refer to Canadian dollars. 2) Registration: Registration fees can be paid in advance by mail. It will also be possible to register on August 17 in the lobby of Burke Science Building. The registration fee covers some of the costs of the conference and entitles you to the reception on Monday night, refreshments during the conference, and registration material. See the attached registration form. The fees are: CATEGORY REGULAR DISCOUNTED (if received by July 15) ---------------------------------------------------------------------- supported $140 $120 regular $70 $60 student $25 $20 The ``supported'' category applies to any non student whose travel is supported by his university or some other agency. The regular category applies to all the rest of the non student participants. Students whose participation is not supported by some agency or their university may apply for a waiver of the registration fee and for a reduction of the banquet (see below) charge. Such application should be made to Matt Valeriote, Chair of the Organizing Committee. 3)Accommodation: Campus Residence: On campus accommodation in Woodstock Hall is available to all participants. This residence features single and twin bedded rooms with centralized washroom facilities. Those interested are asked to complete the relevant portion of the enclosed registration form and send it in by July 15 with FULL PAYMENT to The Alan Day Conference: attn P. Penny Department of Mathematics and Statistics McMaster University 1280 Main Street West Hamilton, Ontario CANADA L8S 4K1 Only those requests accompanied by full payment will be confirmed. Refunds will be granted if written notice of cancellation has been received by 12 noon on Friday August 14, 1992. Cancellations are subject to a $10.00 administrative fee. For those who wish to extend their visit, residence rooms will be available before the 16th as well as after the 22nd. The rates are: $37.18 per person, per night - Single Occupancy $31.53 per person, per night - Double Occupancy and include hot breakfast, daily maid service, bed linens, towels, soap, parking and all relevant taxes. Participants staying in the campus accommodations are asked to register at the Housing Registration Desk located in the Commons Building - Main Lobby where they will receive their room assignments and parking pass. The desk is open from 7:00am to 12 midnight daily. Hotels: A block of rooms has been reserved at reduced rates at the Royal Connaught Hotel. The nightly rate is $77.00 plus tax (5% provincial room tax and 7% federal tax). If you wish to stay at this hotel, please indicate so on the accommodations form and a reservation will be made for you. The Royal Connaught is located in downtown Hamilton and is easily accessible by public transportation from McMaster University. Royal Connaught Hotel 112 King Street East Hamilton, Ontario L8N 1A8 (416)-527-5071, FAX (416)-527-2751 4)Transportation: Hamilton is located on the south-western shore of Lake Ontario, approximately 70 kilometres from Toronto. It is served by Pearson International Airport (Toronto) as well as by Mount Hope Airport (Hamilton). Most participants will choose to land at Pearson where Airways Transit operates a door-to-door van service to and from Hamilton. This service will take you from Pearson Airport to whichever place in Hamilton you need to go. Most will wish to be taken to the Commons Building at McMaster or the Royal Connaught Hotel. The special one-way conference fare for this service is $21.50 including all taxes. If you wish to make use of this service, it will be necessary to make a reservation. Please send the conference organizers the enclosed Ground Transportation Registration Form as soon as you have booked your flight to Toronto so that we can make this reservation for you. Upon arrival at Pearson Airport, proceed to the Ground Transportation Booth and make yourself known to the personnel there. The trip to McMaster University from Pearson Airport will take approximately 1 hour. You will be required to pay the driver the full fare in cash. If you are flying to Mount Hope, the taxi fare into the city is about $25.00 (for up to 4 passengers). Phone numbers of companies offering trips to and from Mount Hope are: (416)-628-8282 and (416)-679-4828. A map will be enclosed in the paper mailing for use by those driving to Hamilton. It will show the major highways into the city, together with exit ramp instructions and local directions. Those driving to McMaster should enter the campus on the east side, via Sterling Street. From Monday to Friday, they will be charged a deposit by the Parking Attendants at the kiosk at the entrance to the campus. Those staying in residence will be reimbursed at the Housing Registration Desk for the parking charge and issued a parking pass valid for the duration of the Conference. All vehicles must be parked in ZONE 1 lot and parking passes displayed on the dashboard. 5)Social Activities: On the evening of the 17th, there will be a reception for all participants in the lounge area of Woodstock Hall. This reception will begin about 7:30pm. On Thursday evening a banquet will be held at the Faculty Club at McMaster University. The price for this banquet will be $30 not including alcoholic beverages. The banquet will be preceded by a cocktail hour (cash bar). Special dietary needs will be accommodated if we are notified in advance. Those interested in attending are asked to indicate so on the enclosed registration form. You will be required to pay for the banquet no later than Monday, August 17. This is to ensure that an adequate number of spaces are reserved. You can pay any time before then as well. An excursion to Niagara Falls has been organized for Wednesday afternoon, August 19. Buses will leave for Niagara in the early afternoon and arrive in about 1 hour's time. The bus will return to Hamilton in the early evening. The cost of this trip will be $16.00 per person to cover the cost of the bus. If you are interested in participating, please indicate so on the registration form. Tickets for this trip can be purchased on Monday morning, August 17, or payment can be included with the registration fees. Space for the excursion is limited, and space for the banquet is somewhat limited. So priority will be given to those who reply on the registration form. Higher priority will be given to those who include payment with such a reply. Information about the many other attractions in the Hamilton area will be available during the conference. A special note to those who may wish to attend the Stratford Shakespeare Festival or the Niagara-on-the-Lake Shaw Festival: it is advisable to purchase tickets for the performances well in advance. This can be done by telephone, using a credit card. To contact the Shakespeare festival ticket office, dial (519)-273-1600 and to contact the Shaw Festival ticket office, dial (416)-468-2172. 6)Other Details: The weather is generally pleasant in August, usually around 25 degrees Celsius. Rain is not uncommon, nor is high humidity. The cost of cigarettes is extremely high, as is the cost of liquor, so we advise those who plan to consume these items while at the conference to purchase them duty free before entering Canada. There are many hiking and jogging trails and the university athletic facilities will be available to participants. . -------------------------CUT-HERE------------------------------------------ The Alan Day Conference REGISTRATION FORM Name (Prof./Dr./M_): affiliation: Mailing Address: Telephone: E-mail address: FAX: I am a student at the following university:________________________ ACCOMMODATIONS I wish to stay at the Royal Connaught Hotel. YES______ NO________ (Note: A reservation will be made for you, but payment will need to be made to the hotel upon arrival. Cancellations must be received by 12 noon on Friday, August 14, 1992.) I wish to stay in the campus residences. YES______ NO________ (Only those requests accompanied by full payment will be confirmed.) ROOM INFORMATION: My arrival date will be _____________________, and my departure date will be ___________________________. I am male/female: __________________. I desire a single room _________________. I desire a double room _____________, and my preferred roomate is ___________________________________________. I am a smoker____________ non-smoker_________________, and I am willing to room with a smoker____________ non-smoker_________________. Others will be traveling with me, the total number in my party including myself is _____________, and, all together, we will need ________________ single rooms and _______________ double rooms. SOCIAL EVENTS Niagra Falls Excursion: I wish to reserve ___________________ places on this excursion at $16.00 per place. (If payment is not enclosed, it must be paid at the registration desk upon arrival and no later than noon on Monday, August 17, 1992.) Banquet at the Faculty Club on Thursday evening, August 20, 1992: I wish to reserve __________________ places at this banquet at $30.00 per place (If payment is not enclosed, it must be paid at the registration desk upon arrival and no later than noon on Monday, August 17, 1992.) SPECIAL REQUESTS OR NEEDS Please note any you have here. FEES ENCLOSED Registration Fees: CATEGORY REGULAR DISCOUNTED (if received by July 15) ------------------------------------------------------ supported $140 $120 regular $70 $60 student $25 $20 amount enclosed $_____________ Campus Accommodations: single @ $37.18/day x number of days _______ x number of rooms _______ = $_____________ double @ $31.18/person/day x number of days _______ x number of people _______ = $_____________ Social Events: Niagra Excursion @ $16.00/person x No. of people _____ = $_____________ Banquet @ $30.00/person x number of people _________ = $_____________ TOTAL AMOUNT ENCLOSED = $______________ Your cheque should be payable to: McMaster University. It should be for Canadian dollars or the equivalent amount in U.S. dollars. (If you send U.S. dollars, please be generous when calculating the equivalent amount so that the conference doesn't lose money because of exchange rate fluctuations and the cost of the exchange.) Mail the completed form and your cheque to: The Alan Day Conference c/o Mrs. Pamela Penny, C.A.M. Administrative Coordinator Department of Mathematics and Statistics McMaster University 1280 Main Street West Hamilton, Ontario L8S 4K1 CANADA ---------------------------CUT-HERE------------------------------------------- The Alan Day Conference GROUND TRANSPORTATION RESERVATION FORM Please supply the following information so we can make reservations for you with Airways Transit for your travel between Pearson Airport in Toronto and Hamilton. NAME:___________________________________________________________ NUMBER IN PARTY:_____________________ ARRIVAL DATE:______________________ ARRIVING FROM:_________________ AIRLINE & FLIGHT NO.: _______________________ TIME:__________________ DEPARTURE DATE:____________________ DEPARTING TO:__________________ AIRLINE & FLIGHT NO.: _______________________ TIME:__________________ ------------------------------------------------------------------ FOR OFFICE USE ONLY: Date made:___________________________ By:_____________________________ Pick-up time:________________________ From:__________________________ ------------------------------------------------------------------- Mail the completed form to: The Alan Day Conference c/o Mrs. Pamela Penny, C.A.M. Administrative Coordinator Department of Mathematics and Statistics McMaster University 1280 Main Street West Hamilton, Ontario L8S 4K1 CANADA or FAX it to: (416)-522-0935 or e-mail it to: penny(a)sscvax.cis.mcmaster.ca ---------------------------CUT-HERE------------------------------------------ The Alan Day Conference ABSTRACT FORM This is for a talk_____________ or poster display___________________. (Check one, please.) NAME: TITLE: ABSTRACT: Mail the completed form to: The Alan Day Conference c/o Mrs. Pamela Penny, C.A.M. Administrative Coordinator Department of Mathematics and Statistics McMaster University 1280 Main Street West Hamilton, Ontario L8S 4K1 CANADA or FAX it to: (416)-522-0935 or e-mail it to: alan_program(a)kahuna.math.hawaii.edu or day_prog@@kahuna.math.hawaii.edu or any combination of the above. ------------------------CUT-HERE-------------------------------------- ----[end attachment]---- Fred E.J. Linton Wesleyan U. Math. Dept. 649 Sci. Tower Middletown, CT 06459 E-mail: <FLINTON(a)eagle.Wesleyan.EDU> ( or <fejlinton(a){att|mci}mail.com> ) Tel.: + 1 203 776 2210 (home) or + 1 203 347 9411 x2249 (work)

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adjunctions
by pavlovic＠triples.Math.McGill.CA 21 Apr '92

21 Apr '92

Michael Barr and I came across upon the following elementary fact, which does not seem to have been noticed so far. (However, Michael's conviction that something like this should be true was based on his proof of theorem 3 in "The Point of the Empty Set", Cahiers XIII-4(1972), pp.357-368.) Let A and B be categories, F:A->B and G:B->A functors, h:id->GF and e:FG->id natural transformations. Then F is left adjoint to G as soon as the transformations a = eF.Fh and b = Ge.hG are either both split epi or both split mono. PROOF. First observe that the naturality alone implies eF.aGF = eF.FbF FbF ------------------------------- | | | FhGF FGeF V FGF ----------> FGFGF --------> FGF | | | | | | |id |eFGF |eF | | | V aGF V eF V FGF -----------> FGF ----------> F Now if some (natural!) right inverses a' and b' of a resp. b are given, we derive eF.a'GF = eF.Fb'F Fb'F FbF FGF ----------> FGF ----------> FGF | | | | |a'GF |a'GF | | V FbF V FGF ----------> FGF | | | | |aGF |eF | | V eF V FGF -----------> F The unit and the counit of the adjunction F-|G will be eta = h :id->GF epsilon = e.Fb' :FG->FG->id The adjunction identities follow: (eta)G G(epsilon) G ------------> GFG ----------> G | | | | | | |b' |GFb' |id | | | V (eta)G = hG V Ge V G ------------> GFG ----------> G F(eta) (epsilon)F F ------------> FGF ----------> F | | | | | | | | |a' a'GF| |Fb'F |id | | | | V F(eta) = Fh V V eF V F ------------> FGF ----------> F When a and b are split monics, one can dualize the above arguments by switching e and h; or simply consider the opposite categories of A and B. Regards to all, Dusko Pavlovic =================================================================== Subj: AUTOMATED REASONING JOB From: dfs(a)hilbert.maths.utas.edu.au Junior Research Fellow AUTOMATED REASONING PROJECT Applications are invited for a Junior Research Fellowship at the University of Tasmania for a period of 6 months, starting 15 August 1992, with a possibility of renewal for a similar period. The salary will be in the range: $31980-38,950pa, and a contribution toward the cost of a fare to Tasmania will be made. The successful applicant will join a small group working on an ARC-funded Project entitled: A model and programming language for reasoning incorporating Grobner base methods. Applicants should have an Honours degree in Computer Science or Mathematics, with a major in the other discipline. A strong background in algebra, and practical programming experience are desirable. The principle task of the appointee will be disciplined research programming: to refine, extend and test a programming language for reasoning that currently exists in prototype form, written in Mathematica. The language is based on ideas from algebra, category theory and functional programming. Substantial programming skills will be needed, but experience with Mathematica is not required. The position offers the opportunity to combine creative programming in an exciting project with a taste of life in Tasmania --- if it's not the best life-style in the world, what is? Applicants should forward their Curriculum Vitae to reach The Staff Officer, University of Tasmania, PO Box 252C, Hobart, Tasmania 7001, AUSTRALIA by 25 May 1992. They should also ask three referees to submit letters in support of their application direct to the Staff Officer. All correspondence should quote Ref: 48/92. The University of Tasmania is an equal opportunity employer. Email enquiries about the position, and notice of intention to apply may be addressed to the undersigned. ------------------------ Desmond Fearnley-Sander, Mathematics Department, University of Tasmania, PO Box 252C, Hobart, Tasmania 7001, AUSTRALIA. Phone: 002 202445 Fax: 002 202867 AARnet: dfs(a)hilbert.maths.utas.edu.au ------------------------ ===================================================================

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Diagrammes
by Charles Wells 17 Apr '92

17 Apr '92

Sears Library of Case Western Reserve University now has Diagrammes volumes 1 through 20 (through 1990) on the shelves and has ordered the more recent volumes. It is committed to continuing the subscription. This means that if you are in the USA, at least, you can get copies of articles in it via interlibrary loan. --Charles Wells -- Charles Wells 216 368 2893 ===================================================================

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Pfn again
by Lars Birkedal 07 Apr '92

07 Apr '92

Thanks for the responses to my question concerning Pfn. Barry Jay asked for a "real problem". Here is one from computer science. The following diagram is used in Abstract Interpretation, where a program is modelled extensionally, i.e. V and V' are sets of stores, f is a transition function with dom(f) being a possibly proper subset of V (e.g. a transition function corresponding to one of the branches of an if-statement.) Furthermore a and a' are abstraction functions, and we're interested in the pushout, to get a best possible abstract approximation f' to f. V ---f----> V' | | | | a a' | | | | A---f'---> A' Lars Birkedal (birkedal(a)diku.dk) ===================================================================

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Pfn
by Lars Birkedal 03 Apr '92

03 Apr '92

Does there exist a comprehensive treatment of the category Pfn, objects are sets and morphisms are partial functions - specifically I`m interested to know if someone has proven the existence of colimits and other such concepts in Pfn. Thanks, Lars Birkedal (birkedal(a)diku.dk) =====================================================================

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Workshop -- first announcement
by dbenson＠yoda.eecs.wsu.edu 03 Apr '92

03 Apr '92

Foundational Methods in Computer Science: A workshop on applications of categories in computer science 1992 May 30-31 Sloan Hall School of Electrical Engineering and Computer Science Washington State University, Pullman WA 99164-2752 The focus of this workshop is the applications of categories to computer science. Ernie Manes has agreed to give a lecture on the subject of his new book, "Predicate Transformer Semantics". Robin Cockett will present an introduction to the fascinating work on categorical programming. I hope to convince Steve Bloom to discourse about iteration theories. Here is a list of possible areas, not meant to be in any sense limiting, for those interested in contributing talks of approximately 20 minutes duration: Semantics of programming languages Categorical and functional programming Program specification and verification Proof theory Logics and type theory Linear logics and Concurrency Theory Pedagogy and foundational issues This workshop is informal, even casual, but certain details need early attention so that the workshop goes smoothly. The cost is $US40 regular and $US25 for graduate students. There will be a reception Friday evening and an informal banquet Saturday night, included in this fee. We greatly appreciate receiving advance registrations. Please send a check together with your mailing address and any other particulars which you would like us to notice and attend to before the workshop begins. Pullman banks are only able to accept $US and $CA without disproportionate fees. Please use one of these two currencies. Thanks. As it currently appears that places are limited to about 25, please respond by return email with your intention as soon as may be. If you wish to contribute a talk, please email a tentative title. ------------------Categories in Computer Science------------------------- A one day introduction to categories, as used in typical computer science applications, consisting of six hours of lectures, is being organized for the day of Friday, May 29, just prior to the workshop. The plan is to begin at the beginning, perhaps with the Lawvere-Schanuel notes, Benjamin Pierce's new book with MIT Press, and with Bob Walters' book. If you find this introduction to be of interest and plan to attend, please so indicate in your return email or with your advance registration. Thanks. __-----------------------------------------------------------------__ Travel: Air transportation to Pullman is provided by Horizon Air via Spokane, Seattle, Pasco, Portland and Boise. All of these cities are served by several major airlines. But I recommend flying to Portland, Boise, Seattle or Spokane and renting a car. The scenery is well worth it. Details regarding scenic auto routes will be provided to those requesting further travel information. Note that Mt. Ranier, Mt. St. Helens, the Columbia Gorge, North Cascades Park, Glacier Park, and Yellowstone Park are all within one day's drive -- although not all on the same day. Alternatively, Campus Link, (208) 882-1223, provides airport limo service between Pullman/Moscow and the Spokane airport. Greyhound Bus provides two buses a day from each of Portland, Seattle, and Spokane. Housing: One may car camp in the city park for about ten US dollars a night. We expect to obtain a block of rooms in the vacated student dormitories. The rates are still under negotiation, but appear to be about $26 per person per night for a single and $37 for two in a room per night. These are attractive suites with the bathroom at the end of the hall. A block of rooms has been established for workshop attendees at the American Travel Inn Motel, S 515 Grand Avenue in Pullman. Mention the workshop name, Foundational Methods in Computer Science, when you call (509) 334-3500 to reserve your room, which needs be done before May 15 to obtain the following rates: $US32 single, $US42 double, $US45 4 to a room, all rates subject to a typical hotel tax. The American Travel Inn is about a 20 minute walk from Sloan Hall. Other commercial housing includes: Cougar Land Motel, (509) 334-3535 Hilltop Motor Inn, (509) 334-2555 (Reasonable, but too far to walk) Kimbrough House B+B, (509) 334-3866 (5 minute walk to Sloan Hall) Manor Lodge Motel, (509) 334-2511 (Economical, 10 minute walk to Sloan Hall) Nedels Inn, (509) 332-2646 (10 minute walk to Sloan Hall) In Moscow, 8 miles away, but there is no regular bus service other than Greyhound twice a day. Best Western University Inn, (208) 882-0550; (800) 528-1234 Hillcrest Motel, (208) 882-7579 Mark IV Motor Inn, (208) 882-7557 Motel 6, (208) 882-5511 Peacock Hill B+B, (208) 882-1423 Royal Motel Inn, (208) 882-2581 Super 8 Motel, (208) 883-1503 Looking forward to seeing you at the end of May, Best, David (509) 335-2706 (work) (509) 332-3164 (answering machine at home) dbenson(a)eecs.wsu.edu ===================================================================

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unification
by barr＠triples.Math.McGill.CA 02 Apr '92

02 Apr '92

Paul Taylor gave an example of a unification that he says refuted something he said in Manchester. Unfortunately, it also refutes Theorem 8.7.4 of CTCS. He wrote: > Here is an example of computer science interest, and a counterexample to what > I claimed (privately) at the recent Manchester PSSL. > David Rydeheard's book discusses unification (as used in logic and functional > programming) as a coequaliser in the Kleisli category for the monad for an > algebraic theory with no equations. > A very simple example shows that this is *not* the coequaliser in the > category of algebras. > Take one unary operation f and two variables x,y. Then as a unification > problem the equation f(x)=f(y) implies x=y, but the coequaliser as an algebra > is essentially "N with two zeroes". I ran this example through our proof and found the mistake. On l. 2 of 226 we refer to exercise 3, which says that a map between free algebras for a free theory is either epimorphic or factors through a proper subset of any free generating set. The problem is solved and from the solution, although not from the statement, it is clear that this is true only in the category of free algebras. In fact PT's example gives a trivial counter-example to that too. The map from F1 to F1 that applies f to the generator is epi in the category of free algebras, but not in the category of all algebras; there are two maps from F1 to "N with two zeroes" that agree on the image. Thus the conclusion, that there is a coequalizer, is valid, but only for the category of free algebras. It is not the coequalizer in the algebra category. The statement has to be reworded, but so does the proof because it has to be reworded as a construction of a coequalizer in the Kleisli category. The details are quite easy and we leave it to the reader. Michael ===================================================================

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regepis, stable functors...
by Michel Hebert 02 Apr '92

02 Apr '92

It seems that the following message I sent last March 16 never has been lost somewhere during the trip: ******************************************************* To: CATEGORIES(a)mta.ca Subject: Re: regepis, stablefunctors... Status: RO Answer to Michael Barr. Sorry for having written the other way round what I intended to say in my second paragraph (as remarked by Paul Taylor). Then the algebraically closed fields are a counterexample to your "having a multi- initial object is having an initial object in each slice" precisely because they have the SECOND property but NOT THE FIRST ONE. I suppose you meant "COMPONENT" and not "slice". I think the rest is correct: I said that " in AXIOMATIC categories of finitary models, the existence and preservation by the forg.funct. of pullbacks imply the one of wide pullbacks (and filtered colimits) ". (I meant the theory was also finitary first-order...). In fact it is a classical result of Richter that filtered colimits in such categories are always preserved by the forgetful functor (of course as a result of the existence of the (usual) ultraproducts and elementary substructures). This result was refined by Volger and then (with a result of Pare)we get that the existence of pullbacks and their preservation implies the existence of filtered colimits and also the existence and preservation of cofiltered limits (and hence of "wide pullbacks": those are limits of diagrams with a terminal object). Michel Hebert ===================================================================

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None
by A.Joyal＠dpmms.cambridge.ac.UK 01 Apr '92

01 Apr '92

Cambridge, April 1, 1992 From: Andre Joyal Recently (Feb 12 1992), Colin Mclarty raised up a question about the creation of axiomatic homology theories by Eilenberg and Steenrod. The question is of historical and epistemological interest. He received an answer from Peter Freyd and also from Micheal Barr. The latter suggested to ask Eilenberg directly (I understand that Colin took up the suggestion). Sammy Eilenberg is presently visiting Cambridge and I showed him a copy of the discussion between Mclarty, Freyd and Barr. Sammy made some comments which I reproduce below after recalling the discussion itself. I also added further informations from Sammy. -Andre ------------------------------------------------------------------------- >From CATEGORIES(a)mta.ca Wed Feb 12 04:31:19 1992

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