Recently Riehl and Verity have introduced infinity-cosmoi, which are certain simplicially enriched categories with additional structure. In this paper we investigate those infinity-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 Cauchycomplete 2-cosmoi. Finally, we investigate accessible 2-cosmoi and develop a few aspects of their basic theory.