1 Jan 18:14 2003

### Benabou manuscript


I have seen several references to an unpublished 1973 manuscript by Jean
Benabou on profunctors.

I have had no success finding an e-mail address for Prof. Benabou. Does he
have one?

Peter Johnstone has a very nice synopsis of the subject in his new book in
section B 2.7.  Francis Borceux has a more elementary treatment of
distributors in the first volume of his handbook of categorical algebra.

Are there other sources which offer a substantial discussion of profunctors?

I would be happy to pay duplication and mailing costs to obtain a copy of the
Benabou paper.

Thanks for any information you can provide.

Carl Futia


2 Jan 07:42 2003

### thoughts arising from a letter of Lawvere

Sorting through old papers after the move to our new house, I came
across a communication to Categories by Bill Lawvere, dated 21 Nov 2001,
entitled
"categories:K-spaces and Hurewich", and concerned with the history of
k-spaces and related concepts.
I thought the following bit of history worth contributing.

Before studying monoidal closed categories in his well-known doctoral
thesis, Brian Day wrote a very pleasant Masters thesis on monoidal
closed structures on variants of topological spaces. For some reason
this never got published - perhaps it was not thought original enough at
the time - but it
contained the perfect way of introducing k-spaces; and not just
hausdorff ones - restricting to those is an error.

One starts with the category Top of topological    spaces, and the
category Comp of compact hausdorff spaces. Based on Comp, one forms
Steenrod's category of quasi-spaces: a quasi-space is a set X along
with, for each A in Comp, a subset of Set(A,X) whose elements may be
called the "allowable" maps - one imposes a few evident axioms on these.
The quasi-spaces form a category Qu, whose morphisms from X to Y are
those set-maps whose composites with allowables are allowable.

This is of course classical; but what Brian had is the following. There
is an evident functor f: Top --> Qu; just call A --> X allowable if it
is continuous. There is an equally evident functor
g: Qu --> Top; call a subset open if its characteristic function into
the Sierpinski space 2 lies in Qu. We have the adjunction g --| f. As
with any adjunction, we have an equivalence between the full subcategory
of Top where the counit is invertible and the full subcategory of Qu


5 Jan 00:34 2003

### NASSLLI-2003 ANNOUNCEMENT

 <apologies for multiple postings>

Second North American Summer School
in
Logic, Language and Information
NASSLLI-2003
June 17-21, 2003, Bloomington, Indiana
http://www.indiana.edu/~nasslli

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

The NASSLLI Steering Committee is pleased to announce the Second North
American Summer School in Logic, Language and Information, to be held
in Bloomington, Indiana, June 17-21, 2003.  The event follows on from
the successful first school at Stanford in June, 2002. The school is
focussed on the interfaces among linguistics, logic, and computation,
broadly conceived, and on related fields.  Our sister school, the
European Summer School in Logic, Language, and Information, has been
highly successful, becoming an important meeting place and forum for
discussion for students and researchers interested in the
interdisciplinary study of Logic, Language and Information.  We hope
that the North American schools will follow in this tradition.

PROGRAM
---------

Marco Aiello, Guram Bezhanishvili, and Darko Sarenac
Reasoning about Space (Workshop)

Alexandru Baltag


6 Jan 15:33 2003

### CfP: ESSLLI'03 Student Session


!!! Concerns all students in Logic, Linguistics and Computer Science !!!
!!! Please circulate and post among students !!!
We apologise if you receive this message more than once.

ESSLLI-2003 STUDENT SESSION

SECOND CALL FOR PAPERS

August 18-29 2003, Vienna, Austria

Deadline: February 24, 2003

http://www.science.uva.nl/~bcate/esslli03

We are pleased to announce the Student Session of the 15th European
Summer School in Logic, Language and Information (ESSLLI-2003),
which will be held in Vienna from August 18-29 2003. We invite
submission of papers for presentation at the ESSLLI-2003 Student
Session and for appearance in the proceedings.

PURPOSE:
This eighth ESSLLI Student Session will provide, like the previous
editions, an opportunity for ESSLLI participants who are students to
present their own work in progress and get feedback from senior
researchers and fellow-students.  The ESSLLI Student Session
encourages submissions from students at any level, undergraduates
(before completion of the Master Thesis) as well as postgraduates
(before completion of the PhD degree). Papers co-authored by
non-students will not be accepted.  Papers may be accepted for full


6 Jan 16:14 2003

### BRICS PhD grants and Marie Curie fellowships

[Please accept our apologies if you receive this more than once]

BRICS - Basic Research in Computer Science

at the Universities of  Aarhus  and Aalborg, Denmark

This is a call for applications for:

PhD admission and PhD grants, and
Marie Curie Training Site Fellowships.

BRICS, Basic  Research in  Computer Science, is  funded by  the Danish
National  Research  Foundation.   It  comprises an  International  PhD
School with an associated Research Laboratory.

BRICS  is  based  on  a  commitment to  develop  theoretical  computer
science, covering core areas such as:

- Semantics of Computation,
- Logic,
- Algorithms and Data Structures,
- Complexity Theory,
- Data Security and Cryptology, and
- Verification,

as well as a number of spin-off activities including

- Web Technology,
- Quantum Informatics,
- Bio Informatics, and


7 Jan 03:28 2003

### Hereditarily finite sets


Hello,

I would like to know if anybody is doing research on applying category
theory to hereditarily-finite sets, e.g. where an object is a
hereditarily set with some kind of structure to it and morphism that
preserves that structure. Obviously, the subcategory of SET where
objects
are just hered. finite sets and morphisms are functions between hered.
finite sets is not "interesting". Also, the case where an object is a
hered. set together with an endomorphism doesn't sound "interesting".
I would like URL's of papers if possible. Thank you.

Regards, Bill


7 Jan 15:36 2003

### Category and Scheduling Theory

Hi,

is category theory a suited language to express "structure" in
scheduling or combinatorial optimisation problems ?

Thanks,
Claus


7 Jan 21:08 2003

### Field's Institute Summer School in Logic & Theoretical CS

Dear Colleagues:

June will be theoretical computer science month at U. Ottawa! The
Field's Institute will sponsor a summer school in Logic and
Foundations of Computation at the University of Ottawa this
summer, June 2-20, 2003.  This program will be hosted by the logic
group in the Department of Mathematics and Statistics at the
University of Ottawa  (consisting of Philip Scott, Richard Blute,
and Peter Selinger).

The program will consist of 2 weeks of courses for graduate
students, then a week of workshops in several areas of
theoretical computer science.   This program is particularly aimed
at graduate students in mathematics, logic, theoretical computer
science, mathematical linguistics and related areas. The program
culminates in the 18th annual IEEE Logic in Computer Science
(LICS2003) meeting on campus at U. Ottawa.  For the latter,
see  http://www.dcs.ed.ac.uk/home/als/lics/

The details (and finances) of the Field's program are still being worked
out, but we wanted to alert our colleagues to the following themes:

Weeks 1,2:  Each week will consist of two courses (one in the
morning, the other in the afternoon), taught by experts in the
area.  We are planning topics that include:

Week 1: (a) Categorical Logic and type theory and  (b) Linear Logic.
Week 2:  (a) Game Semantics   and (b) Concurrency.
Week 3:  Workshops.  These include, among other topics,



8 Jan 11:37 2003

### Re: thoughts arising from a letter of Lawvere

I (and a colleague) wonder whether what Max Kelly is referring to is
what Brian Day published in an incredibly concise way in pages 4-5 of
the paper "A reflection theorem for closed categories", J. Pure
Appl. Algebra 2 (1972), no. 1, 1--11.

Max Kelly writes:
> [...]
> This is of course classical; but what Brian had is the following. There
> is an evident functor f: Top --> Qu; just call A --> X allowable if it
> is continuous. There is an equally evident functor
> g: Qu --> Top; call a subset open if its characteristic function into
> the Sierpinski space 2 lies in Qu. We have the adjunction g --| f. As
> with any adjunction, we have an equivalence between the full subcategory
> of Top where the counit is invertible and the full subcategory of Qu
> where the unit is invertible.
>
> The subcategory of Top here, of course reflective in Top, is the
> category of k-spaces, better called the "compactly-generated" spaces; it
> is also a coreflective full subcategory of Qu. Others have noticed this
> since and published it; but certainly subsequent to Brian's 1968 (I
> think) Master's thesis.
> [...]

(We would also be interested in having a copy of the version of the
paper "On quotients maps preserved by product and pullback" before the
translation from category theory to topology (referred to in the
deleted part of Kelly's message). Is that still available?)

Martin Escardo



8 Jan 20:57 2003

### Re: Category and Scheduling Theory

On Tue, Jan 07, 2003 at 03:36:35PM +0100, Claus Gwiggner wrote:
> is category theory a suited language to express "structure" in
> scheduling or combinatorial optimisation problems ?
Yes.  See
R. Bird \& O. de Moor,
\emph{Algebra of Programming},
Prentice Hall Europe, 1997.

Cheers,
David
--

--
Professor David B. Benson                                (509) 335-2706
School of EE and Computer Science (EME 102)              (509) 335-3818 fax
PO Box 642752, Washington State University               office: Sloan 308 and 307
Pullman WA 99164-2752   U.S.A.                           dbenson <at> eecs.wsu.edu
----------------------------------------------------------------------------------



Gmane