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