Abstract: I am Jonathan, and I am interested in connections between logic and higher category theory. In this talk, I am explaining how to reason about fibrations of (∞,1)-categories in a synthetic way. Technically speaking, the logical system used is a version of homotopy type theory (HoTT) which has been extended in 2017 by Riehl and Shulman to provide a convenient setting for reasoning synthetically about Segal and complete Segal aka Rezk spaces. We motivate the basic definitions and state a few familiar theorems that one can prove in this setup, such as a version of the 2-Yoneda Lemma. This is based on joint work with Ulrik Buchholtz and my recent PhD dissertation supervised by Thomas Streicher at TU Darmstadt, Germany.

Link to paper: https://arxiv.org/abs/2105.01724

Subject codes: 03B38, 18N45, 18N60, 18D30, 55U35

Speaker's Contact Information:

Email: weinberger@mathematik.tu-darmstadt.de

Website: https://sites.google.com/view/jonathanweinberger