SIMPLICIAL ∗-MODULES AND MILD ACTIONS

We develop an analogue of the theory of ∗-modules in the world of simplicial sets, based on actions of a certain simplicial monoid EM originally appearing in the construction of global algebraic K-theory. As our main results, we show that strictly commutative monoids with respect to a certain box product on these simplicial ∗-modules yield models of equivariantly and globally coherently commutative monoids, and we give a characterization of simplicial ∗-modules in terms of a certain mildness condition on the EM-action, relaxing the notion of tameness previously investigated by Sagave–Schwede and the first author.