TITLE: Chu(Set,K) without sets ABSTRACT: We define the case V=Set of Chu(V,K) without reference to Set. Somewhat analogously to toposes and abelian categories as 1-categorical abstractions of Set and Ab, we propose rigid couple categories, RCOUP, as a uniform 2-categorical abstraction of the Chu_K categories. Theorem 1 obtains the Chu_K's as the 2-final couple categories of the connected components of RCOUP. Theorem 2 obtains RCOUP as closure of the discrete 2-category of Chu_k's (k the canonical K of that cardinality) under equivalences, subobjects, and 2-cell duplication. One-page extended abstract at http://boole.stanford.edu/pub/couple.pdf The idea for this struck me while preparing my slides for CONCUR last week (any excuse for a break) and so is still in a very preliminary and fluid state. Comments on the perspective welcome. In particular what would you see as being the more natural definition of (ordinary) Chu space: sets A,X and a function r:AxX->K, or an object of a 2-final rigid couple category? Is the latter "what's really going on," or is it just a view of reality distorted by a horribly thick lens, category theory misapplied? Vaughan Pratt