Saturday, March 19, 2011

something about ... the way isbell conjugation as being related to chu construction (and so forth ...) probably makes more sense to me so far than it being related to "spectrum" (or something ... ??...) ideas ... ???hmm, except that in the middle of saying that maybe i sort of see how that second relationship might relate to that first relationship ... ???something about ... ???"duality between geometry and algebra" ... ???"duality between point and function" ... ?? "duality between model and formula" ... ??... and so forth ... ??... ??"satisfaction relation" ... "galois connection" ... ???... ???...

??but anyway ... ??i was going to say something like ... ???let's take some nice more or less familiar "chu construction" situation ... (?? i was thinking for example of concept of "topological space", though now i'm not sure exactly how "pure" an example of such a situation that is... but maybe that's just as well ... or better, or something ... ??...) ... and then ... ??try to think of it in "isbell envelope" terms ... or something ... ???that is, something like ... ??asking what is the thing (... ??...) that we seem to be suggesting the category of topological spaces (or something at least vaguely like that ... or something ... is the "isbell envelope" of??? ... and so forth ... ???...

??maybe also currently more relevant (...??...) examples ... ???something about ... ?"algebraic geometry" ... and so forth ... categorified and/or decategorified ... and so forth ... ???... soemthing about "galois theory" ...

???what about something about non-idempotentness of "isbell envelope" ??? ... and so forth ... ???....

??something about ... "factorization of hom bifunctor" idea ... ??something about "slice and co-slice" ... something about factorization as "interpolation" ... and so forth .... ????....

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