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For a while, I was looking for a Frobenius monad on Set. It doesn't exist as pointed out here. I am now looking at the 2-category of groupoids. Does the 2-category of groupoids admit a Frobenius monad? Does it have a polynomial form?

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  • $\begingroup$ It seems to be the exact same argument that Todd Trimble give in the question you linked will apply to groupoid. At least if you interpret the notion in a 2-categorical sense, though I suspect thing wouldn't be mych different if you interpret things in a stricter sense. $\endgroup$ – Simon Henry Jun 9 at 15:52

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