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Modeling Stable One-Types

By Niles Johnson and Angélica M. Osorno

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.Comment: 18 pages, final versio

Topics: Mathematics - Algebraic Topology, Mathematics - Category Theory, 18B40, 18D10, 55P42, 55S45
Year: 2013
OAI identifier: oai:arXiv.org:1201.2686

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