Abstract
We introduce a new model of connected (n + 1)-types which consists of a subcategory of catn-groups. We study the homotopical properties of this model; this includes an algebraic description of the Postnikov decomposition and of the homotopy groups of its objects. Further, we use this model to build a comparison functor from catn-groups to Tamsamani weak (n + 1)-groupoids which preserves the homotopy type. As an application, we obtain a homotopical semistrictification result for those Tamsamani weak (n + 1)-groupoids whose classifying space is path-connected.
Original language | English |
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Pages (from-to) | 621-727 |
Number of pages | 107 |
Journal | Advances in Mathematics |
Volume | 222 |
Issue number | 2 |
Early online date | 10 Jun 2009 |
DOIs | |
Publication status | Published - 1 Oct 2009 |
Bibliographical note
Funding Information:This work was supported by an Australian Research Council Postdoctoral Fellowship (Project No. DP0558598) held at Macquarie University, where the majority of this work was carried out.
Keywords
- cat-groups
- Homotopy types
- Weak n-groupoid