Exponentiable functors between synthetic $\infty$-categories

Abstract

We study exponentiable functors in the context of synthetic $\infty$-categories. We do this within the framework of simplicial Homotopy Type Theory of Riehl and Shulman. Our main result characterizes exponentiable functors. In order to achieve this, we explore Segal type completions. Moreover, we verify that our result is semantically sound.