Algebraic models for higher categories

作者：Nikolaus Thomas^*

来源：Indagationes Mathematicae, 2011, 21(1-2): 52-75.

DOI：10.1016/j.indag.2010.12.004

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 infinity-groupoids and algebraic quasi-categories as an algebraic model for (infinity, 1)-categories. We furthermore give an explicit proof of the homotopy hypothesis.

• 出版日期2011-7