Date:         Wed, 1 Apr 92 12:00+0100
From:         A.Joyal@dpmms.cambridge.ac.UK


                            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@mta.ca Wed Feb 12 04:31:19 1992
Subject: Steenrod
Date: Tue, 11 Feb 92 13:15:49 -0500
From: cxm7@po.CWRU.Edu (Colin Mclarty)

I understand Steenrod was interested in axiomatizing homology in the 1940s.
An anecdote says that when he first saw category theory he got the idea of
treating maps in homology on a par with homology groups (rather than as a
corollary to the construction of homology groups), and he found this was the
key to axiomatizing the subject.  Does anyone have accurate information on
this?

Colin
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

Message-Id: <920212234300.20601bc0@mta.ca>
Subject: Re: Steenrod
Date: Wed, 12 Feb 92 07:40:22 EST
From: pjf@saul.cis.upenn.edu (Peter Freyd)

In answer to Colin Mclarty's query about Steenrod: one of the first
things he ever told me after he became my dissertation advisor is just
that story.  It had not occured to him to say anything about the action
on maps.  The resulting axiomatization of homology is, of course, his
book with Eilenberg, The Foundations of Algebraic Topology.

He did not deny inventing the phrase "generalized abstract nonsense" to
describe the categorical approach, but he said that it was meant in
the affectionate sense.

Peter
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

Date: Wed, 12 Feb 92 09:36:45 EST
From: barr@triples.Math.McGill.CA (Michael Barr)

The person to ask is Eilenberg.  I heard Sammy tell the following, though.
he said that Steenrod had said to him, upon seeing The general theory
of natural transformations, that no paper had ever influenced his
thinking more.  Sammy also repeated that P.A. Smith, a first rate
algebraic topologist of the ``hard'' school had told him that he
had never read a more trivial paper in his life.  Well, maybe it
wasn't quite so strong.  Sammy thought both reactions quite reasonable.

Certainly, Sammy told some such story about Steenrod wanting to axiomatize
homology theory.  My recollection is that Steenrod told him that although
they knew that there was the homology homomorphism induced by a
continuous map, he had never thought of using that fact as a basis
for his axiomatization.  And that when he read GTNT, the scales fell
from his eyes.  But you should really try to get this story straight
from Sammy.

I suspect that one of the obstacles to taking maps seriously is that
the map induced by an inclusion is not an inclusion.  This must have
bothered people quite a lot in those days.  Homomorphism meant surjective
homomorphism and really only subgroups and quotient groups were taken
seriously.  I have often conjectured that were it not for that,
Birkhoff might have invented categories instead of lattices.

Michael

Remark: I have corrected a mistake at the second line of Mike's message:
he wrote Eilenberg where he obviously meant Steenrod. -Andre J.

-----------------------------------------------------------------------------

The comments by Eilenberg:

>       "Mike Barr recollections are fairly accurate, particularly as
> concerns his first two paragrahs. His third paragraph starting with
> "I suspect ..." is purely speculative. Birchoff did not invented
> lattices, he popularised them."

> In his first paragraph I would cross out the sentence "Well, maybe
> it wasn't quite so strong".

 I add a few recollections obtained from  Eilenberg:

1) W. Hurewicz was the first to use the notation A-->B for a map.
    He used it to denote continuous mappings between spaces as well
    as homomorphisms between groups.(See his 1936 paper refered below)

2) Eilenberg and Steenrod are responsible for choosing the word
   "exact" for naming exact sequences. It is inspired from the work
    of DeRham on differential forms and cohomology. They choosed it
    while writing the Fondation of Algebraic Topology. Before
    agreeing on this terminology they used the word "blank" to avoid
    committing themself to a bad terminology. The terminology
    was adopted immediatly by the mathematical community before
    the appearance of their book (see a paper by Kelly and Pitcher
    which use it before).
    Examples of exact sequences existed before the introduction of the
    terminology  and the notation (See the 1935 paper by Hurewicz
    refered below).

3)A certain amount of commutative diagrams where used before the
    creation of category theory. There is some diagram chasing
    in an abstract of the AMS by Fox around 1940.


References:

Hurewicz W. "Beitrage zur Topologie der Deformationen I" ( Hoher-
dimensionale Homotopiegruppen), Akad. Wetensch. Amster., Proceedings
vol 38, 1935, pages 112-119.

Hurewicz W. "Beitrage zur Topologie der Deformationen IV" ( Aspherical
Raume), Akad. Wetensch. Amster., Proceedings vol 39, 1936, pages 215-224.
===================================================================
Subj:	regepis, stable functors...
Date: Thu, 2 Apr 92 11:14:34 EST
From: Michel Hebert <mhebert@mat.ulaval.ca>

It seems that the following message I sent last March 16 never has been lost
somewhere during the trip:

*******************************************************

To: CATEGORIES@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 

===================================================================
Subj:	unification
Date: Thu, 2 Apr 92 18:43:01 EST
From: barr@triples.Math.McGill.CA (Michael Barr)

 
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
===================================================================
Subj:	Pfn
Date:         Fri, 3 Apr 92 17:08+0100
From:         cbj@dcs.edinburgh.ac.UK


Mike Barr gave a particularly lucid answer to the question of Lars
Birkedale about limits and colimits in Pfn: it is complete and
cocomplete since it is the category of algebras for a triple.

The only problem with this answer is that it fails to take account of
the natural ordering of partial functions (by extension) which is
often of great importance to computer scientists. The difficulties can
be seen with the binary product in Pfn.

The product of two sets A and B in Pfn is given by A+(A\x B)+B whose
three components represent pairs (x,y) in which at least one of x and
y is defined. The problem is that if x<x' and y<y' then it doesn't
follow that (x,y)<(x'y') since the two pairs may both be defined but
take values in different components of the product.

Turning this result around, it is clear that any notion of product
whose pairing *does* preserve the order cannot be the cartesian
product in the usual sense.

Let us re-examine the product from Sets in this context.

First of all it is a local cartesian product. That is, given partial
functions f:C-> A and g:C-> B there is a pair (f,g):C->AxB whose
domain of definition is the intersection of those of f and g. Let p
and q be the projections of the product onto A and B respectively.
Then (writing < for less-than-or-equals) we have

			p.(f,g) < f
			q.(f,g) < g
	If p.h < f and q.h < g then h < (f,g).

This is enough to determine h uniquely, but it does not determine the
object AxB. After all, the empty set would do instead! In order to
capture AxB one must consider its properties in relation to the total
functions. This would be almost tautologous except that it is possible
to define the total morphisms in any ordered category, and so specify
the total functors, natural transformations, adjoints etc, so that the
products arise naturally from the general theory. Details can be found
in my tech. report LFCS 90-107

	Extending properties to categories of partial maps

Total pullbacks, pushouts, etc can all be defined but have yet to be
tested against real problems. Perhaps Lars can help here.

Barry Jay

===================================================================
Subj:	Workshop -- first announcement
Date: Thu, 2 Apr 92 21:01:19 -0800
From: dbenson@yoda.eecs.wsu.edu (David B. Benson)


	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@eecs.wsu.edu

===================================================================
Subj:	Pfn again
Date: Tue, 7 Apr 92 11:46:53 +0200
From: Lars Birkedal <birkedal@diku.dk>

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@diku.dk)
===================================================================
Subj:	Diagrammes
Date: 15 Apr 92   09:20:22 EDT
From: Charles Wells <cfw2@po.cwru.edu>

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

===================================================================
Subj:	Re: Diagrammes
Date:         Thu, 16 Apr 92 12:25+0100
From:         David J Pym <dpym%dcs.edinburgh.ac.UK@QUCDN.QueensU.CA>

Are they any UK libraries with a subscription to Diagrammes ?

djp.
===================================================================
Subj:	re: categories list
Date: 16 April 1992
From: Bob Rosebrugh <RROSEBRUGH@MTA.CA>

For the next two weeks I will be absent and this list will be moderated by my
colleague Daniel Perron. That would not normally be remarked here, but at the
moment faculty at Mount Allison University (including me) have been on strike
for two weeks and there is a possibility that access to computing services may
be suspended. If that were to happen during my absence,  the contingency plan
to move the list to another machine could not be  implemented until May 4, with
a resulting interruption of service. 

Best regards to all, Bob
===================================================================
Subj:	Re: Diagrammes 
Date: Fri, 17 Apr 92 11:39:12 +0900
From: Hiroyuki Miyoshi <miyoshi@slab.sfc.keio.ac.jp>


>> Are they any UK libraries with a subscription to Diagrammes ?
>> 
>> djp.

Also is there Japanese one?
Or does anyone know how to order them?

Hiroyuki Miyoshi
miyoshi@slab.sfc.keio.ac.jp
===================================================================
Subj:	adjunctions
Date: Mon, 20 Apr 92 20:43:13 EDT
From: pavlovic@triples.Math.McGill.CA (Dusko Pavlovic)

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@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@hilbert.maths.utas.edu.au
------------------------

===================================================================
Subj:	Alan Day Conference
Date:    Wed, 29 Apr 1992 12:39:15 -0300 (ADT)
From: "Fred E.J. Linton" <FLINTON@EAGLE.WESLEYAN.EDU>

What follows is Bill Lampe's Second Announcement for the Memorial Conference
honoring Alan Day (of Thunder Bay) to be held at McMaster this August 17-21.

Reproduced here with permission.

---[begin attachment]---

Date: Mon, 20 Apr 92 10:02:01 HST
From: bill@kahuna.math.hawaii.edu
Subject: Alan Day Conference

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@kahuna.math.hawaii.edu
 Department of Mathematics  | BITNET:   william@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@kahuna.math.hawaii.edu
(or
	day_prog@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@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@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@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@eagle.Wesleyan.EDU>     ( or  <fejlinton@{att|mci}mail.com> )
Tel.:         + 1 203 776 2210 (home)      or     + 1 203 347 9411 x2249 (work)
