We discuss the classification of SPT phases in condensed matter systems. We
review Kitaev's argument that SPT phases are classified by a generalized
cohomology theory, valued in the spectrum of gapped physical systems. We
propose a concrete description of that spectrum and of the corresponding
cohomology theory. We compare our proposal to pre-existing constructions in the
literature.Comment: 27 pages, 10 figures. v2: citation updat