On Hopf monads and Hopf adjunctions:
Alain Bruguières, Alexis Virelizier, Hopf monads, Advances in Mathematics 215 2 (2007) 679-733 [doi:10.1016/j.aim.2007.04.011, arXiv:math/0604180]
Alain Bruguières, Steve Lack, Alexis Virelizier, Hopf monads on monoidal categories, Adv. Math. 227 2 (2011) 745-800 [arXiv:1003.1920, doi:10.1016/j.aim.2011.02.008]
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