Okay, still I feel like my understanding of the closure operator is not complete :)
If anybody would be able to shed some light on the following, I would really appreciate.
So I introduced two linear posets P and Q, P consisting of 3 elements, Q of 2, and I also defined left adjoint \\(f\\) (blue) and right adjoint \\(g\\) (orange) as below:


So \\(f.g\\) maps {1, 2} to {1}, and {3} is mapped to {2}. However, \\(f.g.f.g\\) maps {3} to {1}, while {1, 2} are still mapped to {1}. And for me these two operators, \\(f.g\\) and \\(f.g.f.g\\) look quite different, because they produce different mappings, and therefore they cannot be isomorphic to each other.