  Recently Riehl and Verity have introduced $\infty$-cosmoi, which are certain
simplicially enriched categories with additional structure. In this paper we
investigate those $\infty$-cosmoi which are in fact $2$-categories; we shall
refer to these as $2$-cosmoi. We show that each $2$-category with flexible
limits gives rise to a $2$-cosmos whose distinguished class of isofibrations
consists of the normal isofibrations. Many examples arise in this way, and we
show that such $2$-cosmoi are minimal as Cauchy-complete $2$-cosmoi. Finally,
we investigate accessible $2$-cosmoi and develop a few aspects of their basic
theory.
