TITLE: Higher categories as data structures
QUESTION [11 upvotes]: Still wading through higher category theory. I find the subject a bit intimidating, not so much for technical reasons, but because I lack sufficient intuition as to the motivation(s)/heuristics one should use a particular definition instead of another one.
The plethora of formal  possibilities is so great that I would love to have a road map of sorts (such as: if you want to do this, follow this choice, if you wanna do that, here is the menu) 
I do know that there are motivations, for instance in the context of abstract homotopy theory, abstract quantum field theory, etc. 
But I wonder:

from a DATA MODELING's standpoint,
  is there any research geared toward
  using higher cats as advanced data
  structures?

After all, graphs and ordinary 1-dim cats are extremely useful in this respect, so it seems to me that their higher version should also play a big role. 
Any good refs,  thoughts? 
CODA: The ideal situation I have in mind would be something like a nice handbook,  titled
--- higher categories for the working computer scientist--
or
---higher categories  for the working data modeler---.

REPLY [3 votes]: There is work on higher categories and rewriting theory. This considers higher categories as a way of encoding the resolutions of a theory which may itself be of a class of categories. The relevant names are Burroni, Metayer, Lafont, Malbos, Guiraud, so look them up and checkout their preprints etc.