# How to determine whether a map between posets is a fibration

Hey everyone,

is there a good way to determine whether a map of (the topological realizations of) posets is a fibration without explicitely proving that it has the homotopy lifting property?

Robert

• The question doesn't make sense unless you explain what the meaning of fibration of posets is. – John Klein Feb 13 '11 at 4:08
• Well, by a fibration of posets I mean a fibration between their canonical topological realizations. – Robert Feb 13 '11 at 13:23

I just though about this for another minute and it seems like I posted the first part of my question too early. If $f^{-1}(q)$ is contractible, then $f^{-1}(Q_{\leq q})$ is homotopy equivalent to a poset with maximal element, namely the contracted fiber over $q$. Thus, $f^{-1}(Q_{\leq q})$ is contractible.