Algebraic models for higher categories

Details Algebraic models for higher categories Algebraic models for higher categories

2010-03-06

arxiv.org/abs/1003.1342v2

Mathematics

Algebraic Topology

23 pages, minor changes

Scientific paper

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

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