Re: monad: (k-Set \downarrow -): Set -->Set

[Richard Garner <rhgg2@hermes.cam.ac.uk>]

> In the case where k=omega, T is the well-known finite multiset monad,
> which associates to each S the free commutative monoid generated by S
> (whose elements are also known as finite multisets in S).
>
> For other k, I would call this the "monad of multisets of size less
> than k". I think this works for any infinite small cardinal, not just
> regular ones.

You really do need the regularity. Otherwise removing
brackets from a k-small multiset of k-small multisets might
yield something bigger than a k-small multiset, and then one
cannot define a multiplication for the monad.

Richard


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