# Visualizing directed preorders

I am trying to understand directed preorders, a.k.a. directed sets. Are they analogous to connected DAGs?

• One may visualize any preorder as follow. A preorder is a certain type of category. If the category is small, we may take it's nerve. One might also might be able to visualize this as a graph of some sort. – Baby Dragon May 22 '13 at 3:52

Not quite. A DAG cannot have edges $x\to y$ and $y\to x$, while a directed preorder can have $x\leq y$ and $y\leq x$.