Nikolaus, Thomas (2014) Algebraic K-Theory of infinity-Operads. JOURNAL OF K-THEORY, 14 (3). pp. 614-641. ISSN 1865-2433, 1865-5394
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The theory of dendroidal sets has been developed to serve as a combinatorial model for homotopy coherent operads, see [MW07, CM13b]. 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. Using results from [Heu11b] and [BN12] we show that the K-theory groups of D can be realized as homotopy groups of a K-theory spectrum kappa(D).
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | DENDROIDAL SETS; MODELS; Dendroidal sets; K-theory; operads |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 06 Aug 2019 12:45 |
| Last Modified: | 06 Aug 2019 12:45 |
| URI: | https://pred.uni-regensburg.de/id/eprint/9087 |
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