Modeling Stable One-Types

Abstract

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.

18 pages, final version

Cited by in corpus (6)

• Infinite loop spaces, and coherence for symmetric monoidal bicategories
• Brauer groups and Galois cohomology of commutative ring spectra
• The 2-dimensional stable homotopy hypothesis
• K-theory for 2-categories
• Stable Postnikov data of Picard 2-categories
• The low-energy TQFT of the generalized double semion model