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). The advantage of such an equivalence is that it
allows a stratified space to be viewed categorically because popaths, unlike
holink paths (which are easier to study), can be composed. This paper proves
the aforementioned equivalence in the case of Quinn's homotopically stratified
spaces.