2-fold complete Segal operads

Abstract

We define the notion of Cartesian 2-fibrations, and prove a weak analogue of straightening. Using Barwick's notion of operator categories and the notion of a Cartesian 2-fibration, we extend the notion of $\infty$-operads to the $(\infty ,2)$-categorical context. These $(\infty ,2)$-operads are used to define and study 2-rings in the $\infty$-categorical context.

11 pages, comments welcome. Fixed a proof

References in corpus (3)

• Higher Topos Theory
• Stable Infinity Categories
• (Infinity,2)-Categories and the Goodwillie Calculus I