In the study of stratified spaces it is useful to examine spaces of popaths
(paths which travel from lower strata to higher strata) and holinks (those
spaces of popaths which immediately leave a lower stratum for their final
stratum destination). It is not immediately clear that for adjacent strata
these two path spaces are homotopically equivalent, and even less clear that
this equivalence can be constructed in a useful way (with a deformation of the
space of popaths which fixes start and end points and where popaths instantly
become members of the holink).