In ideally exact categories of unital algebras from operadic varieties, the actor equals the algebra iff it is unital, making V1 action representable; unital Poisson algebras are action representable via explicit universal strict general actor.
Montoli, Action accessibility for categories of interest , Theory and Applications of Cat- egories 23 (2010), no
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On the representability of actions of unital algebras
In ideally exact categories of unital algebras from operadic varieties, the actor equals the algebra iff it is unital, making V1 action representable; unital Poisson algebras are action representable via explicit universal strict general actor.