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—.
Best Answer
There is the recent applied category theory work of David Spivak: http://math.mit.edu/~dspivak/informatics/
Particularly, his work on simplicial databases may be of interest to you.