Subject: Another for the list From: Mark Hovey Date: 16 Jul 2005 07:20:36 -0400 I have had an insight about Freyd's generating hypothesis, to which my last question was related. In view of the interest in the generating hypothesis, and also to find out whether this is already known, I am taking the unusual step of announcing this here. The insight is simply this: The p-local version of Freyd's generating hypothesis holds if and only if the homotopy of any p-complete finite spectrum is an injective module over the homotopy of the sphere. An obvious corollary is that if the generating hypothesis is true, maps from an arbitrary spectrum to a p-complete finite spectrum are determined by their effect on homotopy. There are a couple of other corollaries as well. You can find a short preprint of this result at http://hopf.math.purdue.edu/cgi-bin/generate?/Hovey/freyd Mark Hovey