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Bibliographic Details
Main Authors: Lenz, Tobias, Schröter, Anna Marie
Format: Preprint
Published: 2023
Subjects:
Online Access:https://arxiv.org/abs/2307.11002
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author Lenz, Tobias
Schröter, Anna Marie
author_facet Lenz, Tobias
Schröter, Anna Marie
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2307_11002
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Simplicial $*$-modules and mild actions
Lenz, Tobias
Schröter, Anna Marie
Algebraic Topology
55P48 (Primary), 18N40 (Secondary)
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.
title Simplicial $*$-modules and mild actions
topic Algebraic Topology
55P48 (Primary), 18N40 (Secondary)
url https://arxiv.org/abs/2307.11002