Multifunctorial Equivariant Algebraic K-Theory
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arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913297667719168 |
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| author | Yau, Donald |
| author_facet | Yau, Donald |
| contents | A central question in equivariant algebraic K-theory asks whether there exists an equivariant K-theory machine from genuine symmetric monoidal G-categories to orthogonal G-spectra that preserves equivariant algebraic structures. We answer this question positively by constructing an enriched multifunctor K from the G-categorically enriched multicategory of O-pseudoalgebras to the symmetric monoidal category of orthogonal G-spectra, for a compact Lie group G and a 1-connected pseudo-commutative G-categorical operad O. As the main application of its enriched multifunctoriality, K preserves all equivariant algebraic structures parametrized by multicategories enriched in either G-spaces or G-categories. For example, for a finite group G and the G-Barratt-Eccles operad, K transports equivariant E-infinity algebras, in the sense of Guillou-May or Blumberg-Hill, of genuine symmetric monoidal G-categories to equivariant E-infinity algebras of orthogonal G-spectra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_02794 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multifunctorial Equivariant Algebraic K-Theory Yau, Donald Algebraic Topology Category Theory K-Theory and Homology 18M65, 18D20, 19D23, 19L47, 55P43, 55P91 A central question in equivariant algebraic K-theory asks whether there exists an equivariant K-theory machine from genuine symmetric monoidal G-categories to orthogonal G-spectra that preserves equivariant algebraic structures. We answer this question positively by constructing an enriched multifunctor K from the G-categorically enriched multicategory of O-pseudoalgebras to the symmetric monoidal category of orthogonal G-spectra, for a compact Lie group G and a 1-connected pseudo-commutative G-categorical operad O. As the main application of its enriched multifunctoriality, K preserves all equivariant algebraic structures parametrized by multicategories enriched in either G-spaces or G-categories. For example, for a finite group G and the G-Barratt-Eccles operad, K transports equivariant E-infinity algebras, in the sense of Guillou-May or Blumberg-Hill, of genuine symmetric monoidal G-categories to equivariant E-infinity algebras of orthogonal G-spectra. |
| title | Multifunctorial Equivariant Algebraic K-Theory |
| topic | Algebraic Topology Category Theory K-Theory and Homology 18M65, 18D20, 19D23, 19L47, 55P43, 55P91 |
| url | https://arxiv.org/abs/2404.02794 |