Classification of homotopy $n$-types has focused on developing algebraic categories which are equivalent to categories of $n$-types. We expand this theory by providing algebraic models of homotopy-theoretic constructions for stable one-types. These include a model for the Postnikov one-truncation of the sphere spectrum, and for its action on the model of a stable one-type. We show that a bicategorical cokernel introduced by Vitale models the cofiber of a map between stable one-types, and apply this to develop an algebraic model for the Postnikov data of a stable one-type.
Keywords: stable homotopy one-type, Picard groupoid
2010 MSC: 18B40, 18D10, 55P42, 55S45
Theory and Applications of Categories, Vol. 26, 2012, No. 20, pp 520-537.