I am very curious to study arXiv:1310.7930 (henceforth:DCCT) but am not sure if I have the pre-requisites. I am familiar with basic algebraic topology (singular cohomology, classifying spaces, characteristic classes), differential geometry (bundles, connections, Chern--Weil theory) and some elementary homotopy theory (model categories, spectra, generalised cohomology theories). I am comfortable with the Physics aspects (classical and quantum field theories).
However it appears that in order to understand DCCT, I should know the basics of
- Homotopy Type Theory
- Higher Toposes
- Infinity categories
I have no clue about these subjects. A detailed study of each of these subjects appears to be a humongous task. So I wish to study these subjects with a view to learn as much is necessary for DCCT (and possibly slightly more).
My questions are:
1. What are the subjects which I should familiarise myself with, in order to be able to read DCCT?
(I am not sure if my listing above is accurate, I am just guessing by a glance at the TOC.)
2. Could you please suggest a roadmap to learning the required basics for a person with my background?
As far as possible, I prefer to try to learn stuff linearly and minimise back-and-forth. So a roadmap of pre-requisites would be of great help.
It would be very kind and helpful if you could give pointed references to specific chapters instead of whole books. Thanks a lot!