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Alexander Gietelink Oldenziel (May 15 2023 at 09:20):I have recently been obsessed with cumulants.
They seem to pop up all over the place - super fundamental.
One way to think about them is that the n-th cumulant of a probability distribution is something like the pure n-th order taylor expansion.
There are also connection with Feynmann diagrams and path integrals I believe.
This bring me to my question: is there a way to think categorically about cumulants?
One way people like to think about cumulants is by looking at the cumulant generating function
If I hear about generating functions I think Joyal Species.... is there a way to think about cumulants in terms of Species?
John Baez (May 15 2023 at 15:37):I know a relation between factorial moments and species: