Abstract
We introduce the notion of algebraic fibrant objects in a general model category and establish a (combinatorial) model category structure on algebraic fibrant objects. Based on this construction, we propose algebraic Kan complexes as an algebraic model for ∞ -groupoids and algebraic quasi-categories as an algebraic model for ( ∞ , 1 ) -categories. We furthermore give an explicit proof of the homotopy hypothesis.
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