Simplicial $*$-modules and mild actions
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.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2023
- DOI:
- 10.48550/arXiv.2307.11002
- arXiv:
- arXiv:2307.11002
- Bibcode:
- 2023arXiv230711002L
- Keywords:
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- Mathematics - Algebraic Topology;
- 55P48 (Primary);
- 18N40 (Secondary)
- E-Print:
- Minor corrections and improvements following a referee report. 27 pages