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.

26 pages. Split from previous version of arXiv:2202.12386. Submitted

References in corpus (2)

• Univalent categories and the Rezk completion
• Limits and colimits of synthetic $\infty$-categories