This actually raises another issue with \\(\mathrm{Ob}\\).

Namely, since \\(\mathbf{Set}\\) is itself a category, we uncomfortably get this case,

\\[
\mathbf{Cat}(\mathrm{Disc}(S),\mathbf{Set})
\cong
\mathbf{Set}(S,\mathrm{Ob}(\mathbf{Set})).
\\]