Algebraic K-Theory of infinity-Operads
Abstract
The theory of dendroidal sets has been developed to serve as a combinatorial model for homotopy coherent operads by Moerdijk and Weiss. An infinity-operad is a dendroidal set D satisfying certain lifting conditions. In this paper we give a definition of K-groups K_n(D) for a dendroidal set D. These groups generalize the K-theory of symmetric monoidal (resp. permutative) categories and algebraic K-theory of rings. We establish some useful properties like invariance under the appropriate equivalences and long exact sequences which allow us to compute these groups in some examples. We show that the K-theory groups of D can be realized as homotopy groups of a K-theory spectrum K(D).
Keywords
Cite
@article{arxiv.1303.2198,
title = {Algebraic K-Theory of infinity-Operads},
author = {Thomas Nikolaus},
journal= {arXiv preprint arXiv:1303.2198},
year = {2014}
}
Comments
22 pages, final version, accepted for publication in Journal of K-theory