Homotopical algebra is not concrete

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 $\mathcal{M}$, its homotopy category $\text{ho}(\mathcal{M})$ cannot be concrete. This result is part of an attempt to understand more deeply the relation between set theory and abstract homotopy theory.

arXiv commentFinal version, accepted for publication on Journal of Homotopy and Related Structures