Univalence for inverse EI diagrams

Abstract

We construct a new model category presenting the homotopy theory of presheaves on "inverse EI $(\infty,1)$-categories", which contains universe objects that satisfy Voevodsky's univalence axiom. In addition to diagrams on ordinary inverse categories, as considered in previous work of the author, this includes a new model for equivariant algebraic topology with a compact Lie group of equivariance. Thus, it offers the potential for applications of homotopy type theory to equivariant homotopy theory.

30 pages. v2: updated references to Boavida, small fixes. v3: condensed, reorganized, and clarified exposition; final version to appear in HHA