Another little point: Vaughan credits me with characterizing Wilson space as a final co-algebra. Well, not the topological space. What I wrote in that first posting was: Just for comparison, consider the category of posets and the functor that sends X to X;1;X. The open interval is an invariant object for this functor but it is not the final coalgebra. For that we need -- as we called it in Cats and Alligators -- Wilson space. Actually, not the space but the linearly ordered set, most easily defined as the lexicographically ordered subset, W, of sequences with values in {-1, 0, 1} consisting of all those sequences such that for all n a(n) = 0 => a(n+1) = 0 (take a finite word on {-1,1} and pad it out to an infinite sequence by tacking on 0s). There is, indeed, a functor on Top that delivers Wilson _space_, to wit, the one that sends X to the scone of X + X. 26-Nov-2004 13:34:47 -0400,3185;000000000000-00000000
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Peter Freyd