I am trying to teach myself category theory and, as a beginner, I am looking for
examples that I have a hands-on experience with.

Almost every introductory text in category theory contains following facts.

1. The class of all posets with isotone maps is a category (called $Pos$).
2. Every individual poset $P$ is a category, with comparable pairs $x\leq y$ as arrows. This can be called "a categorified poset".

Sometimes, product and coproduct in $Pos$ is characterized and (less frequently) it is pointed out that a [Galois connection](http://en.wikipedia.org/wiki/Galois_connection) can be characterized as a pair of adjoint functors of categorified posets. Also, it
is sometimes mentioned that products and coproducts in categorified posets are joins
$\vee$ and meets $\wedge$, so a categorified poset has products and coproducts iff it is
a latttice. 

Moreover, some texts contain the fact that the category of finite posets and the category of finite distributive lattices are dually equivalent -- this is extremely useful.

But I cannot find much more. For example, when I tried to search for equalizers and coequalizers in $Pos$, the only source I found is the 
PhD thesis by Pietro Codara, available [here](http://www.cody.it/pietro.php?piepage=research), which is from 2004 and characterizes (co)equalizers
in $Pos$.

Does anyone know about some other sources of information about $Pos$ from the category-theoretic viewpoint?
Specifically, I am looking for things like

 * useful functors to $Pos$ and from $Pos$,
 * pullbacks, pushouts and other universal constructions in $Pos$,
 * examples of adjoint functors, applications of Yoneda lemma etc.