English

The Equivalence Extension Property and Model Structures

Category Theory 2017-08-29 v4 Algebraic Topology Logic

Abstract

We give an elementary construction of a certain class of model structures. In particular, we rederive the Kan model structure on simplicial sets without the use of topological spaces, minimal complexes, or any concrete model of fibrant replacement such as Kan's Ex^infinity functor. Our argument makes crucial use of the glueing construction developed by Cohen et al. in the specific setting of certain cubical sets.

Keywords

Cite

@article{arxiv.1704.06911,
  title  = {The Equivalence Extension Property and Model Structures},
  author = {Christian Sattler},
  journal= {arXiv preprint arXiv:1704.06911},
  year   = {2017}
}

Comments

v4: made main theorem statement self-contained, minor reorganization of corollaries, fixed typos

R2 v1 2026-06-22T19:24:53.889Z