Univalence for inverse EI diagrams

TL;DR

This paper develops a new model category framework for presheaves on inverse EI $( abla,1)$-categories, incorporating universe objects satisfying Voevodsky's univalence axiom, with applications to equivariant algebraic topology.

Contribution

It introduces a novel model for inverse EI $( abla,1)$-categories that includes universe objects satisfying univalence, extending previous work to equivariant contexts.

Findings

Constructed a new model category for presheaves on inverse EI $( abla,1)$-categories.

Includes universe objects satisfying Voevodsky's univalence axiom.

Provides a framework for applying homotopy type theory to equivariant homotopy theory.

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.