(Lack of) Model Structures on the Category of Graphs
Algebraic Topology
2022-04-29 v2 Combinatorics
Category Theory
Abstract
In this article, we study model structures on the category of finite graphs with -homotopy equivalences as the weak equivalences. We show that there does not exist an analogue of Str\o{}m-Hurewicz model structure on this category of graphs. More interestingly, we show that this category of graphs with -homotopy equivalences does not have a model structure whenever the class of cofibrations is a subclass of graph inclusions.
Cite
@article{arxiv.1902.09182,
title = {(Lack of) Model Structures on the Category of Graphs},
author = {Shuchita Goyal and Rekha Santhanam},
journal= {arXiv preprint arXiv:1902.09182},
year = {2022}
}
Comments
minor typos are corrected and a few definitions are added. To appear in the Applied Categorical Structures