Picard groupoids and $\Gamma$-categories
Category Theory
2020-03-13 v2 Algebraic Topology
K-Theory and Homology
Abstract
In this paper we construct a symmetric monoidal closed model category of coherently commutative Picard groupoids. We construct another model category structure on the category of (small) permutative categories whose fibrant objects are (permutative) Picard groupoids. The main result is that the Segal's nerve functor induces a Quillen equivalence between the two aforementioned model categories. Our main result implies the classical result that Picard groupoids model stable homotopy one-types.
Cite
@article{arxiv.2002.05811,
title = {Picard groupoids and $\Gamma$-categories},
author = {Amit Sharma},
journal= {arXiv preprint arXiv:2002.05811},
year = {2020}
}
Comments
arXiv admin note: substantial text overlap with arXiv:1811.11333, arXiv:1908.05668