$U: \text{Pos} \to \text{Set}$ creates directed colimits, what about colimits? Very direct question.
The forgetful functor $U: \text{Pos} \to \text{Set}$ creates directed colimits, what about colimits?
I think the answer is no, but still looking for a counterexample.
 A: It preserves coproducts, but does not reflect them, as there are multiple poset structures on $A\sqcup B$ which are not disjoint. 
For preordered sets, the forgetful functor would preserve all colimits, but since the indiscrete preset has a rather dramatic failure of antisymmetry, we must predict the forgetful functor from posets has no right adjoint. (Indeed, since the representables $0$ and $0\leq 1$ in presets, seen as a full subcategory of graphs, are actually posets, one computes that a putative right adjoint to $U$ would have to be the indiscrete preset. By the locally presentable adjoint functor theorem $U$ must fail to preserve colimits.)
Thus we are led to look for pushouts in presets, the reflection of which into posets destroys information. A simple example is the pushout of two "free arrow" posets $0\leq 1$ along inclusions of the two-object discrete poset which identifies 0 to 1 and 1 to 0. The resulting preset is a cycle $a\leq b\leq a$, which reflects to the terminal poset, so the comparison map for this colimits with respect to $U$ is the projection from two points to one. This rather degenerate behavior is an argument in favor of presets over posets for categorical work.
