On the equivalence between Lurie's model and the dendroidal model for infinity-operads

Gijs Heuts, Vladimir Hinich, Ieke Moerdijk

Research output: Contribution to journalArticlepeer-review

Abstract

We compare two approaches to the homotopy theory of ∞-operads. One of them, the theory of dendroidal sets, is based on an extension of the theory of simplicial sets and ∞-categories which replaces simplices by trees. The other is based on a certain homotopy theory of marked simplicial sets over the nerve of Segal's category Γ. In this paper we prove that for operads without constants these two theories are equivalent, in the precise sense of the existence of a zig-zag of Quillen equivalences between the respective model categories.

Original languageAmerican English
Pages (from-to)869-1043
Number of pages175
JournalAdvances in Mathematics
Volume302
DOIs
StatePublished - 22 Oct 2016

Keywords

  • Dendroidal sets
  • Forest sets
  • Infinity-operads
  • Quillen equivalence
  • Quillen model structures
  • Simplicial operads

All Science Journal Classification (ASJC) codes

  • General Mathematics

Fingerprint

Dive into the research topics of 'On the equivalence between Lurie's model and the dendroidal model for infinity-operads'. Together they form a unique fingerprint.

Cite this