Subject: globular and cubical multiple categories Date: Thu, 20 Dec 2001 12:40:23 +0000 From: Ronnie Brown To: dmd1@lehigh.edu Don, Here is a note for the topology list. PS. Your question on the Hawaiian Earring was in the end too hard for me to think about with all this higher dimensional (and other) stuff buzzing around! Also, after being seriously ill at the beginning of the year, I am getting back to near normality brain wise if that was ever normal! Best wishes Ronnie %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% We would like to draw attention to the following paper Title: Multiple categories: the equivalence of a globular and a cubical approach Authors: Fahd A.A. Al-Agl, Ronald Brown and Richard Steiner (38 pages) which has just been accepted by Advances in Mathematics and for which the latest version is on the arXive at http://arXiv.org/abs/math.CT/0007009 This paper verifies a conjecture from the late 1980s. Its area is that of categorical structures, but it could also be of interest to topologists because of the use of techniques of cubical sets with connection, an area which still has interesting problems, for example geometric realisations of cartesian products. An advantage of the cubical approach is to give an easy description of a monoidal closed category structure for cubical multiple categories, and hence of `higher lax transformations', and so to put the problem for the corresponding globular case onto the explicit description of and calculation with the equivalence. Ronnie -- Professor Emeritus R. Brown, School of Informatics, Mathematics Division, University of Wales, Bangor Dean St., Bangor, Gwynedd LL57 1UT, United Kingdom Tel. direct:+44 1248 382474|office: 382681 fax: +44 1248 361429 World Wide Web: home page: http://www.bangor.ac.uk/~mas010/ (Links to survey articles: Higher dimensional group theory Groupoids and crossed objects in algebraic topology) Raising Public Awareness of Mathematics CDRom Version 1.1 http://www.bangor.ac.uk/~mas010/CDadvert.html Symbolic Sculpture and Mathematics: http://www.cpm.informatics.bangor.ac.uk/sculmath/ Centre for the Popularisation of Mathematics http://www.cpm.informatics.bangor.ac.uk/