Infinity categories with duality and hermitian multiplicative infinite loop space machines
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2016
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| _version_ | 1866913767036551168 |
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| author | Heine, Hadrian Lopez-Avila, Alejo Spitzweck, Markus |
| author_facet | Heine, Hadrian Lopez-Avila, Alejo Spitzweck, Markus |
| contents | We show that any preadditive infinity category with duality gives rise to a direct sum hermitian K-theory spectrum. This assignment is lax symmetric monoidal, thereby producing E-infinity ring spectra from preadditive symmetric monoidal infinity categories with duality. To have examples of preadditive symmetric monoidal infinity categories with duality we show that any preadditive symmetric monoidal infinity category, in which every object admits a dual, carries a canonical duality. Moreover we classify and twist the dualities in various ways and apply our definitions for example to finitely generated projective modules over E-infinity ring spectra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1610_10043 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Infinity categories with duality and hermitian multiplicative infinite loop space machines Heine, Hadrian Lopez-Avila, Alejo Spitzweck, Markus K-Theory and Homology Algebraic Topology Category Theory 19G38 We show that any preadditive infinity category with duality gives rise to a direct sum hermitian K-theory spectrum. This assignment is lax symmetric monoidal, thereby producing E-infinity ring spectra from preadditive symmetric monoidal infinity categories with duality. To have examples of preadditive symmetric monoidal infinity categories with duality we show that any preadditive symmetric monoidal infinity category, in which every object admits a dual, carries a canonical duality. Moreover we classify and twist the dualities in various ways and apply our definitions for example to finitely generated projective modules over E-infinity ring spectra. |
| title | Infinity categories with duality and hermitian multiplicative infinite loop space machines |
| topic | K-Theory and Homology Algebraic Topology Category Theory 19G38 |
| url | https://arxiv.org/abs/1610.10043 |