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arXiv · 2307.11002

Simplicial $*$-modules and mild actions

Tobias Lenz·Anna Marie Schröter
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Abstract

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.

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Tobias Lenz, Anna Marie Schröter. 2023-07-20. Simplicial $*$-modules and mild actions. https://doi.org/10.4310/hha.2024.v26.n2.a12

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