Outputs (2)

The long exact sequence of homotopy n-groups (2023)
Journal Article
Buchholtz, U., & Rijke, E. (2023). The long exact sequence of homotopy n-groups. Mathematical Structures in Computer Science, 33(Special Issue 8: Homotopy Type Theory 2019), 679-687. https://doi.org/10.1017/S0960129523000038

Working in homotopy type theory, we introduce the notion of n-exactness for a short sequence F→E→BF→E→B of pointed types and show that any fiber sequence F↪E↠BF↪E↠B of arbitrary types induces a short sequence

Fn−1 En−1 Bn−1

that is n-exact at... Read More about The long exact sequence of homotopy n-groups.

Synthetic fibered (∞,1)-category theory (2023)
Journal Article
Buchholtz, U., & Weiberger, J. (2023). Synthetic fibered (∞,1)-category theory. Higher Structures, 7(1), 74-165. https://doi.org/10.21136/HS.2023.04

We study cocartesian fibrations in the setting of the synthetic (∞,1)-category theory developed in simplicial type theory introduced by Riehl and Shulman. Our development culminates in a Yoneda Lemma for cocartesian fibrations.