On the question of rectification, see some papers by Jean-Marc Cordier and myself. A good start is J.P.A.A. 67 (1990) 111-124, and then follow up references. The basic input is the theory of homotopy coherence as developed by R.Vogt, Math Z. 134 (1973)11-52. The rectification is a very special case of some of the constructions in his work with Boardman, [SLNM 347,1973]. Cordier{Cahiers, 23 (1982) 93-112] translated this to a simplicial context, so rectification becomes a coherent Kan extension in our paper[Math.Proc. Camb.Phil.Soc. 100(1986)65-90]. We have almost finished a sequel"doing" homotopy coherent category theory using a theory of coherent ends. The combinatorics are quite fun!!! With this theory, I think that it is relatively easy to answer Doug Ravenels question. Tim Porter, School of Mathematics, University College of North Wales, Bangor, Gwynedd, LL57 1UT, U.K. e-mail:mas013@uk.ac.bangor.vaxc P.S. If anyone wants more details, just contact me. =============================