On Hopf monoids in duoidal categories

Aguiar and Mahajanʼs bimonoids A   in a duoidal category MM are studied. Under certain assumptions on MM, the Fundamental Theorem of Hopf Modules is shown to hold for A if and only if the unit of A determines an A-Galois extension. Our findings are applied to the particular examples of small groupoids and of Hopf algebroids over a commutative base algebra.