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I created inner product of multisets, which I hope will help make some sense of some speculations over at the discussion of magnitude of metric spaces.
Thank you Toby for your help on my personal wikiweb.
You're welcome!
The solution turned out to be very pretty. What do you think? It is rare I can contribute something technical, so I'm happy at the moment :)
I fixed a typo and added a note to the end.
It's a rig regardless of cardinalities, since arithmetic of arbitrary cardinal numbers is riggish.
Neat :)
Thanks. I added a section "Machine Learning" with a reference to the n-Cafe.
By the way, the reason I'm looking into this is that I'm trying to relate it somehow to the cardinality of the colimit of a Set-valued functor as I outlined here. It would be neat if your discussion about kernel methods became relevant to weighted colimits (which are categorified integrals).
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