Dear Colleagues This is to announce the availability at http://www-math.mpce.mq.edu.au/~mbatanin/Bigomega.ps of a short 10 page note which begins as follows: ********************************************************************** "The universal property of the multitude of trees" Michael Batanin and Ross Street Macquarie University, N S W 2109 AUSTRALIA Email <mbatanin@mpce.mq.edu.au> and <street@mpce.mq.edu.au> November 1997 Lawvere [BL] essentially pointed out that the category Delta, whose objects are finite ordinals and whose arrows are order-preserving functions, is the generic monoidal category containing a monoid. Let Mon be the category of monoids in the category Set of sets. B�nabou [Be] pointed out that the (simplicial) nerve of the category Delta is the standard resolution [BB] of the terminal monoid via the comonad generated by the underlying functor Mon --> Set and its left adjoint. Let Omcat denote the category of omega-categories and let Glob denote the category of globular sets. In this note we announce a generic property of the category BigOmega whose nerve is the standard resolution of the terminal omega-category via the comonad generated by the underlying functor Omcat --> Glob and its left adjoint. We also give a concrete model for BigOmega in terms of trees. Furthermore, we make connections with the recent work of Joyal [J]. Full proofs of our claims will appear elsewhere. ************************************************************************** Regards, Michael Batanin and Ross Street