Montreal's progress in weak categories (notes on Joyal's and Hermida's talks and Joyal-Street's conversations)

Michael Batanin – 29 October 1997

This talk was based on my impressions of the Montreal conference in September 1997 (Billfest), especially the talks and conversations about higher dimensional category theory. So there were 3 subjects I was talking about: The categories of disks and trees of A.Joyal. The category BigOmega as proposed by R.Street. The result is: Bigomega is the generic monoidal globular category containing a globular monoid. C.Hermida's construction of a bicategory Span_H ( where H is a shape or cartesian monad ) and how to get the higher order operads in my sense from this construction (this result was obtained in the conversations of A.Joyal and R.Street and independently by T.Leinster).