Homology, Homotopy and Applications

Volume 17 (2015)

Number 2

The univalence axiom for elegant Reedy presheaves

Pages: 81 – 106

DOI: https://dx.doi.org/10.4310/HHA.2015.v17.n2.a6


Michael Shulman (Department of Mathematics and Computer Science, University of San Diego, California, U.S.A.)


We show that Voevodsky’s univalence axiom for homotopy type theory is valid in categories of simplicial presheaves on elegant Reedy categories. In addition to diagrams on inverse categories, as considered in previous work of the author, this includes bisimplicial sets and $\Theta_n$-spaces. This has potential applications to the study of homotopical models for higher categories.


homotopy type theory, univalence axiom, elegant Reedy category

2010 Mathematics Subject Classification

03G30, 18G55, 55U35

Published 3 December 2015