Algebraic models for higher categories
Algebraic Topology
2011-05-31 v2 Category Theory
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 oo-groupoids and algebraic quasi-categories as an algebraic model for (oo,1)-categories. We furthermore give an explicit proof of the homotopy hypothesis.
Cite
@article{arxiv.1003.1342,
title = {Algebraic models for higher categories},
author = {Thomas Nikolaus},
journal= {arXiv preprint arXiv:1003.1342},
year = {2011}
}
Comments
23 pages, minor changes