May's Conjecture on Bimonoidal Functors and Multiplicative Infinite Loop Space Theory
Algebraic Topology
2024-05-20 v1 Category Theory
K-Theory and Homology
Abstract
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.
Cite
@article{arxiv.2405.10834,
title = {May's Conjecture on Bimonoidal Functors and Multiplicative Infinite Loop Space Theory},
author = {Donald Yau},
journal= {arXiv preprint arXiv:2405.10834},
year = {2024}
}
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27 pages