The language of∞-categories provides an insightful new way of expressing many results in
higher-dimensional mathematics but can be challenging for the uninitiated. To explain what …

We prove the conjecture that any Grothendieck $(\infty, 1) $-topos can be presented by a
Quillen model category that interprets homotopy type theory with strict univalent universes …

Proof assistants based on dependent type theory provide expressive languages for both
programming and proving within the same system. However, all of the major …

We prove normalization for (univalent, Cartesian) cubical type theory, closing the last major
open problem in the syntactic metatheory of cubical type theory. Our normalization result is …

We begin by recalling the essentially global character of universes in various models of
homotopy type theory, which prevents a straightforward axiomatization of their properties …

Cubical type theory provides a constructive justification to certain aspects of homotopy type
theory such as Voevodsky's univalence axiom. This makes many extensionality principles …

We define and develop two-level type theory (2LTT), a version of Martin-Löf type theory
which combines two different type theories. We refer to them as the 'inner'and the 'outer'type …

The theory of program modules is of interest to language designers not only for its practical
importance to programming, but also because it lies at the nexus of three fundamental …

Yoneda's lemma for internal higher categories Page 1 YONEDA’S LEMMA FOR INTERNAL
HIGHER CATEGORIES LOUIS MARTINI Abstract. We develop some basic concepts in the theory …

Directed type theory is an analogue of homotopy type theory where types represent
categories, generalizing groupoids. A bisimplicial approach to directed type theory …