Subject: categories: Preprint: The co-Birkhoff theorem

From: [email-masked] (Jesse F. Hughes)
Date: 30 Oct 2000 16:56:30 -0500

This is to announce that a pre-print is available at
http://www.contrib.andrew.cmu.edu/user/jesse/papers/CoBirkhoff.ps.gz.
Dusko's recent post regarding coinduction raises a question that is
answered in this paper.  Namely, what is the dual to Birkhoff's HSP
theorem?

Title: The Coalgebraic Dual of Birkhoff's Variety Theorem
Authors: Steve Awodey and Jesse Hughes
Abstract: 

   We prove an abstract dual of Birkhoff's variety theorem for
   categories $\E_\Gamma$ of coalgebras, given suitable assumptions on
   the underlying category $\E$ and suitable $\map\Gamma\E\E$.  We
   also discuss covarieties closed under bisimulations and show that
   they are definable by a trivial kind of coequation -- namely, over
   one ``color''.  We end with an example of a covariety which is
   \emph{not} closed under bisimulations.

   This research is part of the Logic of Types and Computation project
   (http://www.cs.cmu.edu/Groups/LTC/) at Carnegie Mellon University
   under the direction of Dana Scott.

-- 
Jesse Hughes