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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2307.11002 |
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| _version_ | 1866915070236164096 |
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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 |