Normed symmetric monoidal categories
Abstract
Let $G$ be a finite group. In this paper, we study $G$categories equipped with an ordinary symmetric monoidal structure, together with a set of specified norm maps. We give an example and explain how the HillHopkinsRavenel norm functors arise from it, and then we generalize the KellyMac Lane coherence theorem to include the present structures. As an application, we obtain finite presentations of $N_\infty$$G$categories for any $G$indexing system. We also prove coherence theorems for normed symmetric monoidal functors and natural transformations, and we show that normed symmetric monoidal categories are essentially determined by the indexing systems generated by their sets of norms.
 Publication:

arXiv eprints
 Pub Date:
 August 2017
 arXiv:
 arXiv:1708.04777
 Bibcode:
 2017arXiv170804777R
 Keywords:

 Mathematics  Algebraic Topology;
 Mathematics  Category Theory;
 55P91 (Primary) 18D10 (Secondary)
 EPrint:
 44 pages, v2. Sections 6 and 7 have been added for use in the sequels