Homology, Homotopy and Applications
Volume 17 (2015)
The univalence axiom for elegant Reedy presheaves
Pages: 81 – 106
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