We show that a Hopf monad on a *-autonomous category lifts *-autonomous structure to the category of algebras precisely when there is an algebra structure on the dualizing object. Our proof is based on Pastro's characterization of *-autonomous (co)monads as linearly distributive (co)monads with negation.
Keywords: monoidal categories, linearly distributive categories, $*$-autonomous categories, comonoidal monads, Hopf monads
2010 MSC: 18C20,18D10,18D15
Theory and Applications of Categories, Vol. 33, 2018, No. 37, pp 1145-1157.