Abstract
We introduce a new model of connected ( n + 1 ) -types which consists of a subcategory of cat n -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 cat n -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.
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