We show that Voevodsky's univalence axiom for intensional 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 Θn-spaces. This has
potential applications to the study of homotopical models for higher
categories.Comment: 25 pages; v2: final version, to appear in HH
