English

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.

Keywords

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

R2 v1 2026-06-21T14:54:26.886Z