# Examples of universal constructions in probability theory

I am looking for more examples of universal constructions in probability theory. Like the construction a of Gaussian space from a real Hilbert space, or a Poisson jump process from a measurable space with a $\sigma$-finite measure. There must be tons of examples, even though their universality (in the sense of category theory) is probably not commonly emphasized.

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–  Martin Brandenburg Feb 5 '13 at 19:06
@Martin: Thanks! –  UwF Feb 6 '13 at 8:43
I'm not sure that is what you are interested, but there has been much work on projective limits of probability spaces, starting with work of Bochner, as a genralization of the Daniell-Kolmogorov-construction of stochastic processes. –  Michael Greinecker Feb 6 '13 at 14:20
I was thinking of examples that could convince classical probabilists that it might be worthwile for them to study some basic category theory... but I might be dreaming ;) –  UwF Feb 6 '13 at 15:39
It is clearly not an answer, but it is related : a categorical approach to measure theory. –  Pece Dec 7 '13 at 14:40