May's Conjecture on Bimonoidal Functors and Multiplicative Infinite Loop Space Theory
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913354288726016 |
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| author | Yau, Donald |
| author_facet | Yau, Donald |
| contents | A conjecture of May states that there is an up-to-adjunction strictification of symmetric bimonoidal functors between bipermutative categories. The main result of this paper proves a weaker form of May's conjecture that starts with multiplicatively strong symmetric bimonoidal functors. As the main application, for May's multiplicative infinite loop space machine from bipermutative categories to either E-infinity ring spaces or E-infinity ring spectra, multiplicatively strong symmetric bimonoidal functors can be replaced by strict symmetric bimonoidal functors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_10834 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | May's Conjecture on Bimonoidal Functors and Multiplicative Infinite Loop Space Theory Yau, Donald Algebraic Topology Category Theory K-Theory and Homology 18M05, 18M50, 19D23, 55P48 A conjecture of May states that there is an up-to-adjunction strictification of symmetric bimonoidal functors between bipermutative categories. The main result of this paper proves a weaker form of May's conjecture that starts with multiplicatively strong symmetric bimonoidal functors. As the main application, for May's multiplicative infinite loop space machine from bipermutative categories to either E-infinity ring spaces or E-infinity ring spectra, multiplicatively strong symmetric bimonoidal functors can be replaced by strict symmetric bimonoidal functors. |
| title | May's Conjecture on Bimonoidal Functors and Multiplicative Infinite Loop Space Theory |
| topic | Algebraic Topology Category Theory K-Theory and Homology 18M05, 18M50, 19D23, 55P48 |
| url | https://arxiv.org/abs/2405.10834 |