Axiomatization of infinity-categories

I'll discuss our proposed axiomatization of synthetic categories that allows to develop most of (infinity-)category theory from first principles, without relying on explicit set-theoretic models. We expect that such a synthetic theory can make it easier to practice (infinity-)category theory for non-experts and teach it to beginners; moreover, it lends itself to formalization in proof assistants. This talk is based on ongoing collaborative work with D.-C. Cisinski, K. Nguyen and T. Walde.