  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.

Category Theory;Algebraic Topology;Logic