# ct.class idea – Does the understanding of a Poisson monad live? Answer

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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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