Open Access
Translator Disclaimer
2007 Dendroidal sets
Ieke Moerdijk, Ittay Weiss
Algebr. Geom. Topol. 7(3): 1441-1470 (2007). DOI: 10.2140/agt.2007.7.1441


We introduce the concept of a dendroidal set. This is a generalization of the notion of a simplicial set, specially suited to the study of (coloured) operads in the context of homotopy theory. We define a category of trees, which extends the category Δ used in simplicial sets, whose presheaf category is the category of dendroidal sets. We show that there is a closed monoidal structure on dendroidal sets which is closely related to the Boardman–Vogt tensor product of (coloured) operads. Furthermore, we show that each (coloured) operad in a suitable model category has a coherent homotopy nerve which is a dendroidal set, extending another construction of Boardman and Vogt. We also define a notion of an inner Kan dendroidal set, which is closely related to simplicial Kan complexes. Finally, we briefly indicate the theory of dendroidal objects in more general monoidal categories, and outline several of the applications and further theory of dendroidal sets.


Download Citation

Ieke Moerdijk. Ittay Weiss. "Dendroidal sets." Algebr. Geom. Topol. 7 (3) 1441 - 1470, 2007.


Received: 16 May 2007; Accepted: 15 June 2007; Published: 2007
First available in Project Euclid: 20 December 2017

zbMATH: 1133.55004
MathSciNet: MR2366165
Digital Object Identifier: 10.2140/agt.2007.7.1441

Primary: 55P48, 55U10, 55U40
Secondary: 18D10, 18D50, 18G30

Rights: Copyright © 2007 Mathematical Sciences Publishers


Vol.7 • No. 3 • 2007
Back to Top