Homology, Homotopy and Applications

Volume 10 (2008)

Number 1

On the homotopy theory of $n$-types

Pages: 305 – 325

DOI: http://dx.doi.org/10.4310/HHA.2008.v10.n1.a13


Georg Biedermann (Max-Planck-Institut für Mathematik, Bonn, Germany)


We achieve a classification of $n$-types of simplicial presheaves in terms of $(n-1)$-types of presheaves of simplicial groupoids. This can be viewed as a description of the homotopy theory of higher stacks. As a special case we obtain a good homotopy theory of (weak) higher groupoids.


homotopy, simplicial set, simplicial groupoid, simplicial presheaf, simplicial sheaf, stack, Postnikov section

2010 Mathematics Subject Classification

18D05, 18F20, 54B40, 55P15, 55U40

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