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})).

\\]

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})).

\\]