Linear Distributivity With Negation, Star-Autonomy, and Hopf Monads

Masahito Hasegawa and Jean-Simon P. Lemay

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.

Published 2018-11-16.

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