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Modeling stable one-types

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Niles Johnson, Angélica M. Osorno

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.

Published 2012-09-24.

http://www.tac.mta.ca/tac/volumes/26/20/26-20.dvi

http://www.tac.mta.ca/tac/volumes/26/20/26-20.ps

http://www.tac.mta.ca/tac/volumes/26/20/26-20.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/26/20/26-20.dvi

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/26/20/26-20.ps

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