# 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.

• – Martin Brandenburg Feb 5 '13 at 19:06
• @Martin: Thanks! – UwF Feb 6 '13 at 8:43
• 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
• @UwF Now that the dust has settled, what is your take on your own "dream"? That is, what would be some "examples that could convince classical probabilists that it might be worthwile for them to study some basic category theory"? – Did Sep 28 '13 at 9:01
• It is clearly not an answer, but it is related : a categorical approach to measure theory. – Pece Dec 7 '13 at 14:40