Probability and category theory.

[eve11]

Anything up with that? My co-workers are computer scientists and apparently category theory is useful for such study as related to computer languages like Haskell.

There is a parallel out there between categories and probability distributions.... I wonder if there is an application of 'functors' and isomorphism that would describe sufficiency in terms that computer scientists understand.

This is a note to myself to check this out later. I see for example that categories might need to include some notion of sub-probabilities in order to be "complete" in some sense, and that this means that a category theory relationship to probability is not necessarily one-to-one or whatever. I'm curious though, if there may be a category theoretic basis of applied statistics, that would have different implications of inference than using straight probability theory?

And could this possibly extend to continuous measurement?

Why am I thinking so hard on a Sunday? I have fanfic to write, damn it.

Comments

[skurtchasor.livejournal.com]

I believe that "Category Theory" and "Applied x" are disjoint events, regardless of the value of x.

[eve11]

LOL but then, you should get a computer scientist to explain currying of functions in terms of monoids or whatever. My coworker maintains that its useful in the theory of databases. (?)

[skurtchasor.livejournal.com]

Ask said coworker to give an example of a non-academic application written in Haskell (and then duck for cover).