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.
Bibliographical noteFunding 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.
- Homotopy types
- Weak n-groupoid