The constructive Kan-Quillen model structure: two new proofs
Algebraic Topology
2022-06-30 v3 Category Theory
Abstract
We present two new proofs of Simon Henry's result that the category of simplicial sets admits a constructive counterpart of the classical Kan-Quillen model structure. Our proofs are entirely self-contained and avoid complex combinatorial arguments on anodyne extensions. We also give new constructive proofs of the left and right properness of the model structure.
Cite
@article{arxiv.1907.05394,
title = {The constructive Kan-Quillen model structure: two new proofs},
author = {Nicola Gambino and Christian Sattler and Karol Szumiło},
journal= {arXiv preprint arXiv:1907.05394},
year = {2022}
}
Comments
Revised version, 52 pages. Minor improvements in exposition. New statements Lemma 1.1.1 and Lemma 1.2.1. Accepted for publication in Quarterly Journal of Mathematics