Homotopical algebra is not concrete
Category Theory
2025-08-05 v4 Algebraic Topology
Logic
Abstract
We generalize Freyd's well-known result that "homotopy is not concrete", offering a general method to show that under certain assumptions on a model category , its homotopy category cannot be concrete. This result is part of an attempt to understand more deeply the relation between set theory and abstract homotopy theory.
Keywords
Cite
@article{arxiv.1704.00303,
title = {Homotopical algebra is not concrete},
author = {Fosco Loregian and Ivan Di Liberti},
journal= {arXiv preprint arXiv:1704.00303},
year = {2025}
}
Comments
Final version, accepted for publication on Journal of Homotopy and Related Structures