Homology, Homotopy and Applications

Volume 23 (2021)

Number 2

Rigidification of dendroidal infinity-operads

Pages: 349 – 372

DOI: https://dx.doi.org/10.4310/HHA.2021.v23.n2.a18


Peter Bonventre (University of Kentucky, Lexington, Ky., U.S.A.)

Luís A. Pereira (Duke University, Durham, North Carolina, U.S.A.)


We give an explicit description of the rigidification of an $\infty$-operad as a simplicial operad. This description is based on the notion of dendroidal necklace, extending work of Dugger and Spivak from the categorical context to the operadic context, although with a different framework, which relates constructions involving necklaces to a standard factorization of maps in the category of trees.


operad, dendroidal set

2010 Mathematics Subject Classification

18-xx, 55P91

Received 26 April 2020

Accepted 24 September 2020

Published 15 September 2021