Big Omega available

Big Omega available

[categories]

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Date: Thu, 27 Nov 1997 10:31:13 +1100
From: Ross Street <street@mpce.mq.edu.au>

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.  Bénabou [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