Simplicial $*$-modules and mild actions

Tobias Lenz, Anna Marie Schröter

Research output: Working paperPreprintAcademic


We develop an analogue of the theory of $*$-modules in the world of simplicial sets, based on actions of a certain simplicial monoid $E\mathcal M$ 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 $E\mathcal M$-action, relaxing the notion of tameness previously investigated by Sagave-Schwede and the first author.
Original languageEnglish
Number of pages27
Publication statusPublished - 20 Jul 2023


  • math.AT
  • 55P48 (Primary), 18N40 (Secondary)


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