Dendroidal segal spaces and ∞-operads

Denis Charles Cisinski*, Ieke Moerdijk

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


We introduce the dendroidal analogues of the notions of complete Segal space and of Segal category, and construct two appropriate model categories for which each of these notions corresponds to the property of being fibrant. We prove that these two model categories are Quillen equivalent to each other, and to the monoidal model category for 8-operads which we constructed in an earlier paper. By slicing over the monoidal unit objects in these model categories, we derive as immediate corollaries the known comparison results between Joyal's quasi-categories, Rezk's complete Segal spaces, and Segal categories.

Original languageEnglish
Pages (from-to)675-704
Number of pages30
JournalJournal of Topology
Issue number3
Publication statusPublished - Sept 2013


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