Homology, Homotopy and Applications
Volume 10 (2008)
On the homotopy theory of $n$-types
Pages: 305 – 325
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