Date: Thu, 24 Apr 1997 15:37:19 +1100 From: Ross Street This is to announce the placement on the WWW of the notes of my two lectures at the Conference on Higher Category Theory and Mathematical Physics, Northwestern University (Evanston, Illinois; 28-30 March 1997). The site is: [I have tried to eliminate offending fonts and to accommodate funny US paper size. Thanks to Sjoerd Crans for helping here.] Title: The role of Michael Batanin's monoidal globular categories Lecture I: Globular categories and trees Lecture II: Higher operads and weak omega-categories This is a report on recent work of Michael Batanin. The goal of his work is to provide an environment for defining the concepts associated with weak omega-categories and for developing the ensuing theory. The approach is "globular". To put this in context, I might mention some important steps in the development of weak omega-categories. Categories were defined by Eilenberg-Mac Lane in 1945. Monoidal and symmetric monoidal categories were defined by Mac Lane in 1963. Ehresmann defined (strict) n-categories in 1966. Bénabou defined bicategories in 1967. In the early 80s, monoidal bicategories were in the air but a full definition was not published in that period. Joyal-Street defined braided monoidal categories in 1985. Gordon-Power-Street defined tricategories in 1991 (this, and the coherence theorem, were published in 1995). Braided monoidal categories were defined by Kapranov-Voevodsky-Baez-Neuchl-Breen around 1993. Trimble produced a definition of tetracategory in 1995. Diverse approaches to weak n-categories for all n have appeared. Street (1985) suggested a simplicial definition with horn filler conditions. Trimble (1994) approached the problem using operads and Stasheff associahedra. Baez-Dolan (1995) have a definition using typed operads and opetopes. Tamsamani (1996) gave a multisimplicial definition. Batanin uses higher operads and globular sets. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Ross Street email: street@mpce.mq.edu.au Mathematics Department phone: +612 9850 8921 Macquarie University fax: +612 9850 8114 Sydney, NSW 2109 Australia Internet: http://www.mpce.mq.edu.au/~street/ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~