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Dear All,
I hope all is well.
I thought you might find how the mathematics of questions informs quantum measurements as elucidated in my good friend's recent original work The Mathematics of Questions of some interest.
Thanking you,
Yours respectfully,
posina
P.S. Just in case a question of 'what's categorical in it?' arises: The process of going from propositions to their corresponding combinations of questions and answers lends itself to be construed (on my superficial reading) as a functor going from the category S of sets (of propositions) to a category S/L of labelled sets, whose objects are functions: Questions --> Answers, with Answers = {no, yes} as the labelling set L. This functor S --> S/L has an adjoint functor S/L --> S. Of course, there are groups and more that readily lend themselves to categorical readings.