1 Sep 2005 13:53

### Re: Preprint: A simple description of Thompson's group F

  There's a good chance that the characterization of Thompson's group F
(not to mention its name) was set forth in the paper reviewed below
(the authors of which became aware of R.J.Thompson's priority via
this review).

Freyd, Peter; Heller, Alex
Splitting homotopy idempotents. II.
J. Pure Appl. Algebra 89 (1993), no. 1-2, 93--106.

A preliminary version of this paper was in the reviewer's hands in
1979 and was then of uncertain age. The authors have done a service in
publishing it (in somewhat revised form) belatedly.

The object of study is a free homotopy idempotent $f \colon X \to X$;
this means that $f$ is freely (base point not necessarily preserved
during the homotopy) homotopic to $f^2 \equiv f \circ f$. This $f$ is
said to split if there are maps $d \colon X \to Y$ and $u \colon Y \to X$ such that $d \circ u \simeq \text{id}_Y$ and $u \circ d \simeq f$,
where $\simeq$ denotes free homotopy.

They construct a group $F$ and an endomorphism $\phi \colon F \to F$
such that, for a certain $\alpha_0 \in F$, $\phi^2(7) = \alpha^{-1}_0\phi(7)\alpha_0$. The induced map $g \colon K(F,1) \to K(F,1)$ is a homotopy idempotent which does not split; and it is
universal in the sense that it maps "canonically" into any homotopy
idempotent, and the corresponding homomorphism $F \to \pi_1(X)$ is
monic if and only if $f$ does not split.

This group $F$ is shown to be finitely presentable, has simple
commutator subgroup, is a totally ordered group and contains a copy of


1 Sep 2005 19:56

### Preprint: Information integration in institutions

The paper whose abstract is given below is available at

http://www.cs.ucsd.edu/~goguen/pps/ifi04.pdf

and will appear in a memorial volume for Jon Barwise
sometime in 2006, edited by Larry Moss.

Information Integration in Institutions
Joseph A Goguen
Department of Computer Science  and Engineering
University of California at San Diego, USA

This paper unifies and/or generalizes several approaches to information,
including the information flow of Barwise and Seligman, the formal conceptual
analysis of Wille, the lattice of theories of Sowa, the categorical general
systems theory of Goguen, and the cognitive semantic theories of Fauconnier,
Turner, Gardenfors, and others.  Its rigorous approach uses category theory
to achieve independence from any particular choice of representation, and
institutions to achieve independence from any particular choice of logic.
Corelations and colimits provide a general formalization of information
integration, and Grothendieck constructions extend this to several kinds of
heterogeneity.  Applications include modular programming, Curry-Howard
isomorphism, database semantics, ontology alignment, cognitive semantics, and
more.


1 Sep 2005 18:17

### Re: Preprint: A simple description of Thompson's group F

Marcelo and Tom write

We show that Thompson's group F is the symmetry group of the "generic
idempotent".  That is, take the monoidal category freely generated by an
object A and an isomorphism A \otimes A --> A; then F is the group of
automorphisms of A.

Tom has pointed out to me that the review of the old Freyd/Heller I
posted give no hint of its relevance. Therefor this:

F was defined (40 years ago) as the initial model for a group with
an endomorphism that's conjugate to its square.

More formally: consider the equational theory that adds to the theory
of groups a constant, s, and a unary operator  e, subject to two
further equations:

e(xy) = (ex)(ey)             "e is a endomorphism"
s(ex) = (e(ex))s             "e is a conjugacy-idempotent"

The initial algebra for this theory is the group  F.

(If one insists on removing the type-error in the last sentence, then
try "the initial algebra for this theory when subjected to the
forgetful functor back to groups is  F.")

If one defines a sequence of elements   s_n = e^n(s)  they clearly
generate  F (as a group) and it isn't hard to see that a complete set
of relations for  F (as a group) is the doubly-infinite family



5 Sep 2005 21:44

### CiE 2006, Call for Papers

                               CiE 2006
Computability in Europe 2006 :
Logical Approaches to Computational Barriers
30 June - 5 July 2006
Swansea University
http://www.cs.swansea.ac.uk/cie06/

CALL  FOR  PAPERS

CiE 2006 is the second of a new conference series on Computability
Theory and related topics which started in Amsterdam in 2005.  CiE 2006
will focus on (but not be limited to) logical approaches to
computational barriers:
- practical and feasible barriers, e.g., centred around the P vs. NP
problem;
- computable barriers connected to models of computers and
programming languages;
- hypercomputable barriers related to physical systems.

Tutorials will be given by:
Samuel R. Buss (San Diego)
Julia Kempe (Paris)

Invited Speakers include:
Jan Bergstra (Amsterdam)
Luca Cardelli (Microsoft Cambridge)
Jan Krajicek (Prague)
Elvira Mayordomo Camara (Zaragoza)


5 Sep 2005 16:53

### Eighth International Symposium on Functional and Logic Programming


[FLOPS benefits from an eclectic mix of FP and LP papers, one of the few
venues where the two communities get together.   It should be a
congenial meeting, situated under Mt Fuji.  Do come!   -- P]

First Call For Papers

Eighth International Symposium on Functional and Logic Programming
FLOPS 2006

April 24--26
Fuji Susono, JAPAN

http://hagi.is.s.u-tokyo.ac.jp/FLOPS2006

FLOPS is a forum for research on all issues concerning declarative
programming, including functional programming and logic programming,
and aims to promote cross-fertilization between the two paradigms.
Previous FLOPS meetings were held in Fuji Susono (1995), Shonan
Village (1996), Kyoto (1998), Tsukuba (1999), Tokyo (2001), Aizu
(2002), and Nara (2004).

TOPICS

FLOPS solicits original papers in all areas of functional and logic
programming, including (but not limited to):

Declarative Pearls: new and excellent declarative programs with
illustrative applications;


6 Sep 2005 22:21

### Memorial service for John

On August 10 I received the following information about John Isbell's
death.

A memorial service is now being planned and will most likely occur
at Forest Lawn on Saturday, September 10. No other details are
available now; an obituary should appear in the Buffalo News today
or later this week.

No obit has appeared (paid or ortherwise) and I have not succeeded in
finding any further information about the service.

Does anyone know?

Peter


8 Sep 2005 00:46

### News from Tulane?

Just wondering if anybody here has had any news from our collegues from
Tulane (eg Mike Mislove)?  Are they safe, did they evacuate before the
hurricane, what's in store for them now?  (I know the university is shut -
and I guess probably for the forseeable future, though that's also a
question.)  Obviously one wishes them all the best in this impossibly
difficult time.

-= rags -=

--

--
<rags <at> math.mcgill.ca>
<www.math.mcgill.ca/rags>


8 Sep 2005 13:52

### Noether and fast thinking

Somewhere MacLane published a part of a letter he sent his mother from
Goettingen where he said that Fraulein Noether "thought fast and spoke
faster" or something like that.  I have looked at every mention of
Noether by him that I can think of without re-locating this one.  Does
anyone know where it is?

thanks, Colin


8 Sep 2005 06:44

### Re: Memorial service for John

Hello, Peter, and all Categories readers,

Googling "Buffalo News obituary John Isbell" today brought this up:

> John R. Isbell Ph.D.
>
> August 6, 2005 age 74. Dear father of Margaret M. Thornborough of > Bristol, England, John C. Isbell of
Bloomington, IN, and Brecht W. > Isbell of Los Angeles, CA.; grandfather of Zelie Thornborough and >
Alexander L. L. Thornborough both of England; brother of Frances W. > Isbell of Weslaco, TX and the late
Robert O. Isbell. There will be no > prior visitation. A Memorial Service will be held Saturday, September
> 10, 2005 at 4 PM at the Chapel of Forest Lawn Cemetery. Friends > invited. Mr. Isbell was a Math Professor at
SUNY  <at>  Buffalo from 1969-
> 1999. Arrangements by AMIGONE FUNERAL HOME INC. Online guest register > at www.Amigone.com
>
> Published in the Buffalo News on 8/28/2005.

[URL (all one line; best turn off Active-X):

http://legacy.com/BuffaloNews/LegacySubPage2.asp?Page=LifeStory&PersonI=d=3D14948085

]

------ Original Message ------
Received: Wed, 07 Sep 2005 06:25:08 AM EDT
From: Peter Freyd <pjf <at> saul.cis.upenn.edu>
To: categories <at> mta.ca
Subject: categories: Memorial service for John

> On August 10 I received the following information about John Isbell's
> death.


8 Sep 2005 01:13

### Follow-ups to [HP89]?

In the introduction to their 1989 article,

JME Hyland & AM Pitts, "The Theory of Constructions: Categorical
Semantics and Topos-Theoretic Models", Contemp. Math. 92 (1989), 137
- 199,

the authors say, "Clearly this paper is only a beginning."  Can someone
recommend follow-ups to this paper published in the intervening 15 years?

Todd Wilson
Department of Computer Science
California State University, Fresno



Gmane