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 …

We introduce and study central types, which are generalizations of Eilenberg-Mac Lane
spaces. A type is central when it is equivalent to the component of the identity among its own …

We study localization at a prime in homotopy type theory, using self maps of the circle. Our
main result is that for a pointed, simply connected type $ X $, the natural map $ X\to X_ {(p)} …

We prove the Hurewicz theorem in homotopy type theory, ie that for X a pointed,(n− 1)–
connected type, with n≥ 1, and A an abelian group, there is a natural isomorphism π n (X) …

We develop topics in synthetic homotopy theory using the language of homotopy type
theory, and study their semantic counterparts in an∞-topos. Specifically, we study …

𝐴)× 𝐵 (𝑎), dependent products (𝑎: 𝐴)→ 𝐵 (𝑎), identity types 𝑎= 𝐴 𝑏, empty type 0, unit type
1, coproducts 𝐴+ 𝐵, natural numbers type ℕ, and universes L. If not, good references that …

We study localization at a prime in homotopy type theory, using self maps of the circle. Our
main result is that for a pointed, simply connected type X, the natural map X→ X (p) induces …

We detail our current understanding of Ext groups in homotopy type theory and their
semantic counterparts in a Grothendieck∞-topos. Homotopy type theory can be interpreted …

Localization in HoTT Dan Christensen Joint with M. Opie, E. Rijke, L. Scoccola Outline: Page 1
Localization in HoTT Dan Christensen University of Western Ontario Joint with M. Opie, E …