Bastiaan Cnossen: Synthetic category theory I: General setup

Speaker
Bastiaan Cnossen, University of Regensburg

Abstract
I will present an axiomatic approach to synthetic category theory, joint with D.-C. Cisinski, T. Walde and K. Nguyen. The axioms are formulated in natural language and are ‘model-agnostic’, meaning that they can be interpreted in a wide variety of foundational systems. From these axioms we deduce a large chunk of standard (higher) category theory, including the Yoneda lemma, Quillen’s Theorems A and B, and the complete Segal space perspective on categories. We hope our framework aids formalization of category theory; we will see two approaches towards formalizing our axioms in Tashi’s and Ivan’s talks.