The 2-dimensional stable homotopy hypothesis (Q2001396)

The authors prove the Stable Homotopy Hypotheses (SHH) in dimension 2, i.e., the equivalence of homotopy theories of Picard 2-categories equipped with categorical equivalences and stable 2-types equipped with stable equivalences. The reviewer may add that SSH in dimension 0 is the equivalence of homotopy theories of abelian groups and Eilenberg-Mac Lane spectra and SSH in dimension 1 was described by the second two authors [Theory Appl. Categ. 26, 520--537 (2012; Zbl 1252.18034)].