I must apologize to John, others, and especially Heiner Kamps, for what I wrote on Fri, 21 Feb 1997 and repeated on this Bulletin Board this morning. The construction K' does not do what we want. This means, at the moment, I am stuck with the cohomological construction as the only way I know to prove the result. With the patience of the Bulletin Board, I would like to explain how I made the mistake. A monoidal category is autonomous (or rigid or compact) when each object has a left and right dual. If the category is a groupoid, it suffices that, for each object a there should be an object b with a (tensor) b isomorphic to the unit (these monoidal categories have been called categorical groups). An autonomous monoidal category is called strict when it is strict as a monoidal category and the (contravariant) dualization functor is a strict monoidal isomorphism. By a construction like K', each autonomous monoidal category is monoidally equivalent to a strict autonomous monoidal category. But there are different kinds of strictness. The dual objects in a strict autonomous monoidal category still may not be strict inverses. Sorry, Ross 11-Mar-2002 21:31:36 -0400,2122;000000000000-00000000