Modeling Stable One-Types

Details Modeling Stable One-Types Modeling Stable One-Types

2012-01-12

arxiv.org/abs/1201.2686v1

Mathematics

Algebraic Topology

11 pages

Scientific paper

It is a classical result that groupoids model homotopy 1-types, in the sense that there is an equivalence between the homotopy categories, via the classifying space and fundamental groupoid functors. We extend this to stable homotopy 1-types and Picard groupoids. Using an algebraic description of Picard groupoids, we give a model for the Postnikov invariant of a stable 1-type and describe the action of the truncated sphere spectrum in these terms. We relate this data to exact sequences of Picard groupoids developed by Vitale, constructing a model for the homotopy cofiber of a map of stable 1-types.

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