Homology, Homotopy and Applications

Volume 22 (2020)

Number 1

On $d$-categories and $d$-operads

Pages: 283 – 295

DOI: https://dx.doi.org/10.4310/HHA.2020.v22.n1.a16


Tomer M. Schlank (Mathematics Department, Hebrew University of Jerusalem, Israel)

Lior Yanovski (Mathematics Department, Hebrew University of Jerusalem, Israel)


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

18A99, 55Pxx

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