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ct.class idea – Does the understanding of a Poisson monad live?
Starting with a monoidal class with duals $C$, one could deem the class $End(C)$ of endofunctors of $C$. A Hopf monad on $C$ is a bimonad on $C$ with (a generalised understanding of the) antipode. Under apt assumptions for the Hopf monad, this Hopf monad utilized on the unit objective of the class $C$ is a Hopf algebra within the centre of $C$.
The query is that if the understanding of Poisson monad in $End(C)$ has been outlined someplace? In the illustration that such a understanding exists, does it revert a Poisson algebra objective within the class?
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