On d-categories and d-operads

Tomer M. Schlank*, Lior Yanovski

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We extend the theory of d-categories, which are a strict model for (d, 1)-categories introduced by Lurie, by providing an explicit description of the right mapping spaces of the d-homotopy category of an ∞-category. Using this description, we deduce an invariant ∞-categorical characterization of the d-homotopy category. We then proceed to develop an analogous theory of d-operads, which model ∞-operads with (d-1)-truncated multimapping spaces, and prove analogous results for them.

Original languageAmerican English
Pages (from-to)283-295
Number of pages13
JournalHomology, Homotopy and Applications
Issue number1
StatePublished - 2020

Bibliographical note

Publisher Copyright:
© 2020, International Press.


  • Homotopy theory
  • Infinity-category


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