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We define a notion of groupoidal 2-quasi-categories and show that they arethe fibrant objects of a model structure on the category of $\Theta_2$-sets. Weshow that this model category is Quillen equivalent to the Kan-Quillen modelcategory of simplicial sets and that 2-truncated groupoidal 2-quasi-categoriesare models for homotopy 2-types.

Groupoidal 2-quasi-categories and homotopy 2-types