I have a basic question on the usual model structure on simplicial sets. What is the relation between being a Kan (trivial maybe ?) fibration and surjectivity ? Surjectivity here means either ...
In the definition of a Kan fibration (on nlab), i.e. for a map $\pi:Y\to X$ of simplicial sets the inclusion of any horn into $Y$ always lifts to an inclusion of the filled in horn if that filled in ...