I've got a little confused by some set theory underlying Hopkins-Lurie's survey on classification of topological field theories.
The objects of $(\infty,n)$-categories need to form a set, at least if the definition we take is as some kind of weakened Kan complex. Yet in some examples they give objects clearly do not form sets, for example the $ (\infty,1)$-category of chain complexes $chain_t (k)$.
Is there something I am missing?
Edit: About comment below. I am not sure I understand what Lurie's 1.2.15 says concretely, about the example above. If someone could comment it would be great.