On $\infty$-cosmoi of bicategories

Abstract

An $\infty$-cosmos is a setting in which to develop the formal category theory of $(\infty ,1)$-categories. In this paper, we explore a few atypical examples of $\infty$-cosmoi whose objects are 2-categories or bicategories rather than $(\infty ,1)$-categories and compare the formal category theory that is so-encoded with classical 2-category and bicategory theory. We hope this work will inform future explorations into formal $(\infty ,2)$-category theory.

20 pages; v2 has more detail about the isofibrations in each $\infty$-cosmos and the proof in section 6 replaced by a literature citation