Paper Preprint Available ======================== The following paper preprint is available for anonymous FTP from ftp.mpce.mq.edu.au (137.111.216.12) in /pub/maths/Categories/mod.bicats.ps.Z The abstract is available as /pub/maths/Categories/mod.bicats.abs MODULATED BICATEGORIES. Aurelio Carboni, Scott Johnson, Ross Street, and Dominic Verity ABSTRACT: The concept of regular category has several 2-dimensional analogues depending upon which special arrows are chosen to mimic monics. Here, the choice of the conservative arrows, leads to our notion of faithfully conservative bicategory K in which two-sided discrete fibrations become the arrows of a bicategory F=DFib(K). While the homcategories F(B,A) have finite limits, it is important to have conditions under which these finite ``local'' limits are preserved by composition (on either side) with arrows of F. In other words, when are all fibrations in K flat? Novel axioms on K are provided for this, and we call a bicategory H modulated when H^op is such a K. Thus, we have {\bf constructed} a proarrow equipment ()_*:H-->M (in the sense of Wood) with M=F^coop. Moreover, M is locally finitely cocomplete and certain collages exist. In the converse direction, if M is any locally countably cocomplete bicategory which admits finite collages, then the bicategory M^* of maps in M is modulated. {Recall that a 1-cell in a bicategory is called a {\it map\/} when it has a right adjoint.} --------------------------------------------------------------------------- To fetch and print a copy of the file, use the following procedure: % ftp ftp.mpce.mq.edu.au Name: anonymous Password: <user>@<site.domain> ftp> cd /pub/maths/Categories ftp> binary ftp> get mod.bicats.ps.Z ftp> quit % uncompress mod.bicats.ps.Z % lpr -P<postscript-printer> mod.bicats.ps If your site does not support the Unix uncompress program, or you have trouble fetching compressed files, our server can uncompress the file for you. Simply fetch mod.bicats.ps instead of mod.bicats.ps.Z. --------------------------------------------------------------------------- Dominic Verity, Macquarie University, NSW 2109, Australia. email: domv@macadam.mpce.mq.edu.au ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++