From: categories <cat-dist@mta.ca>
To: categories <categories@mta.ca>
Subject: Big Omega available
Date: Thu, 27 Nov 1997 16:01:49 -0400 (AST) [thread overview]
Message-ID: <Pine.OSF.3.90.971127160137.5834D-100000@mailserv.mta.ca> (raw)
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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
reply other threads:[~1997-11-27 20:01 UTC|newest]
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