Workshop on Computer Algebra Methods and Commutativity of Algebraic Diagrams (CAM-CAD)

IRIT, Toulouse  (France)
16-17 October 2009

*** AND ***

Categorical diagrams have multiple applications in
mathematics (algebra, topology) and computer science (models
and metamodels, rewriting systems, higher order languages). 
Diagrams (understood less strictly) can be found in physics,
chemistry and other scientific domains. Many similar
problems arise in computer-assisted treatment of diagrams in
all these domains. In spite of the importance of
diagrammatic methods, they are relatively little developed
and underrepresented in the world of computer-assisted

This workshop aims to bring together researchers working on
these subjects, to assess the current state of the art and
identify open problems and future research directions.

The main topics may be listed (non-exhaustively) as follows:
algorithms that may be used in computer-assisted treatment
of diagrams, treatment of diagrams in existing computer
algebra systems, formal developments related to diagrams and
category theory in proof-assistants, user interfaces and
graphics for categorical diagrams.

Papers presented at the workshop will be published on the
web site of the workshop (see below) and are planned to be selected for
submission, in complete and revised form, to a special issue
of an international journal.


1. Lucas Dixon (Univ of Edinburgh)

a) Monoidal Categories, Graphical Reasoning, and Quantum Computation, joint work with Aleks Kissinger

b) Basic Elements of Logical Graphs

2. Kosta Dosen and Zoran Petric (Math. Inst., Belgrade)

Monads and Graphs

3. Yves Guiraud (LORIA), Philippe Malbos (Lyon-1)

Identities among relations for higher-dimensional rewriting systems

4. Robert Hein and François Lamarche (LORIA)

Bifibrations and paths in categories.

5. Samuel Mimram (ENS-Lyon)

Computing Critical Pairs in Polygraphs

6. Damien Pous (CNRS)

Untyping Typed Algebraic Structures

7. Andrei Rodin (ENS, Paris - rue d'Ulm)

Diagrammatic syntax and its constraints

8. Pierre Rannou (Inst. Math. de Luminy)

Coassociativity of deconcatenation: a diagrammatic proof

9. A. El Khoury (IRIT), S. Soloviev (IRIT), L. Mehats, M. Spivakovsky (IMT)

On Varieties of Closed Categories and Dependency of Diagrams


Friday 16.10.2009

10 - 10.30 Registration

1O.30 - 11.15

Lucas Dixon

Basic Elements of Logical Graphs

11.15 - 11.35  Coffee Break

11.35 - 12.20

Robert Hein, Francois Lamarche

Bifibrations and Paths in Categories

12.30 - 14.00 Lunch (at the university restaurant)

14 - 14.45

Andrei Rodin

Diagrammatic syntax and its constraints.

14.45 - 15.30

Damien Pous

Untyping Typed Algebraic Structures

15.30-15.50 Coffee Break

15.50 - 16.35

Samuel Mimram

Computing Critical Pairs in Polygraphs

16.35 - 17.20

Yves Guiraud, Philippe Malbos

Identities among relations for higher-dimensional rewriting systems

17.20 - 18 Coffee, Discussion

20 h Conference dinner


Saturday 17.10.2009

10 - 10.45

Pierre Rannou

Coassociativity of deconcatenation: a diagrammatic proof

10.45 - 11 Coffee Break

11 - 11.45

Lucas Dixon and Aleks Kissinger

Monoidal Categories, Graph Reasoning, and Quantum Computation

11.45 - 12.30

A. El Khoury, S. Soloviev, L. Mehats, M. Spivakovsky

On Varieties of Closed Categories and Dependency of Diagrams.


Lunch (in town)

List of participants

Most of the participants are visible on the following two photographs, one taken by Yves Lafont and one taken by Sergei Soloviev right after the end of the workshop.

    IRIT - Université Paul Sabatier 
    118 route de Narbonne 
    F-31062 Toulouse Cedex 9 

The workshop will take place in "Salle de theses" (the room where 
most PhD thesis defenses take place) near the reception at the ground


You have to take underground line B (metro B) direction Ramonville
to the station "Université Paul Sabatier".
Most centrally placed is the  station  "Jean Jaures". (Walking distance
from most of the hotels in the center.)
On the same line are the stations "Jeanne D'Arc" and "Compans-Cafarelli"
(first stop of the airport shuttle coming from the airport and last before
the airport in the direction of airport). Near "Compans-Cafarelli" there
is also a taxi stop (may be useful for return trip). You should count
about 20 min by underground to the university.

If you want to take the metro at the railway station (line A) you go one
stop to "Jean Jaures" and change to line B.

When you go out at "Université Paul Sabatier" you are at the entrance to
the campus. You should follow the small road going slightly downhill
(about 400 m.) and turn to your right as shown in the scheme below:

                route de Narbonne
                     ___________      v
               service building|      v      R
                   ____________|      v      O
                                      v      A
                                      v      D
                   -----------------------|      |------------------
                                     road          road
                  ------------------------       -----------------------
                           T          v       R
                           R          v       O
                           E  parking v   barrier
                           E          v       A
BUILDING                   S          v       D
                        <- -----------
low building          v
                      v                ___________________________
                      v                |
                                       |  Admin. B-g                     
|                     v
    < ----------      v
IRIT 100 m.

You come to the reception of IRIT (IRIT is written also on the wall of the

We will ask for a modest participation fee (30 euros to be
used for 3-4 coffee breaks and a lunch on Friday at the
university restaurant).

We plan to organize an "informal" dinner on Friday evening.

[NOTE: The informal workshop dinner took place at the restaurant "Le
Fazoul", 2 rue Tolosane.]


Submission deadline: we expect a full paper or an extended
abstract by 30 September 2009. As an exception, we may still
consider to extend the list of talks if the full paper or
extended abstract will come (for sure) by 30 september, and
we will be notified before 10 september - as usual, the
message should contain the title and a short abstract.

Workshop: Friday 16 and Saturday 17 October 2009

Organising/program committee:

    P. Damphousse (Universite de Tours)
    Y. Lafont (IML, Universite Aix-Marseille 2)
    R. Matthes  (IRIT, Universite Paul Sabatier, Toulouse)
    S. Soloviev (IRIT, Universite Paul Sabatier, Toulouse)

Local organisation:

    S. Soloviev
    R. Matthes
    A. El Khoury


    Sergei Soloviev
    University Toulouse-3
    118, route de Narbonne,
    31062 Toulouse
    E-mail: soloviev, followed by @irit and then .fr
    Tel:  (+33) 5 61 55 62 55
    Fax: (+33) 5 61 55 62 58

Ralph Matthes