Algebraic models for higher categories

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Abstract: We establish a model category structure on algebraic Kan complexes. In fact, we introduce the notion of an algebraic fibrant object in a general model category (obeying certain technical conditions). Based on this construction we propose algebraic Kan complexes as an algebraic model for -groupoids and algebraic quasi-categories as an algebraic model for -categories.

http://arxiv.org/abs/1003.1342