Actually, thinking about it, we could give a dual presentation by restricting \\(\mathbf{Feas}\\).

Then restricting the posets in \\(\mathbf{Feas}\\) to only sets gives the category \\(\mathbf{Rel}\\) (as I noted above), restricting thre feasiblity relations in \\(\mathbf{Feas}\\) to only monotone functions gives the category \\(\mathbf{Poset}\\), and restricting in both way gives the category \\(\mathbf{Set}\\).

If there was a category \\(\mathbf{Porel}\\) of posets as objects and relations as morphisms, then \\(\mathbf{Feas} \cong \mathbf{Porel}\\) .