Various forms of vertical and horizontal transportation: a photo of the Dusquesne Incline, Pittsburgh
Photo by Joe Ireland via Facebook of the Duquesne Incline, Pittsburgh.
I have written about "social urbanism" in Medellin, Colombia, where the city has constructed escalators and aerial trams in neighborhoods to foster social and economic integration, where topography has traditionally been a barrier.
A public escalator system is also present in Hong Kong.
-- "Transportation infrastructure as civic architecture: Johannesburg and "Corridors of Freedom""
I've also mentioned public elevators that do the same thing, although there don't seem to be many examples, but Monaco is one.
Typically we think of vertical transportation within cities as being exclusively within buildings in private properties, limited to elevators and escalators (and stairs).
These past entries:
-- "Public improvement districts ought to be created as part of transit station development process: the east side of NoMA station as an example"
-- "Hong Kong needs to create a formal and planned pedestrian mobility network"
encourage us to think and plan these networks more systematically.
Besides escalators, stairwells, and elevators. incline elevators/funiculars are another example.