Homology, Homotopy and Applications
Volume 22 (2020)
On $d$-categories and $d$-operads
Pages: 283 – 295
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 $\infty$-category. Using this description, we deduce an invariant $\infty$-categorical characterization of the d-homotopy category. We then proceed to develop an analogous theory of doperads, which model $\infty$-operads with $(d-1)$-truncated multimapping spaces, and prove analogous results for them.
homotopy theory, infinity-category
2010 Mathematics Subject Classification
Copyright © 2019, Tomer M. Schlank and Lior Yanovski. Permission to copy for private use granted.
The first author was supported by the Alon Fellowship and the ISF grant 1588/18. The second author was supported by the ISF grant 1650/15.
Received 20 February 2019
Received revised 28 May 2019
Accepted 8 June 2019
Published 11 December 2019