It would be more appropriate to study it using algebraic geometry; say, etale homotopy theory. See:

Čech Theory: Its Past, Present and Future http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?handle=euclid.rmjm/1250128825&view=body&content-type=pdf_1

Dave

http://alpha.math.uga.edu/~davide/

It would be more appropriate to study it using algebraic geometry; say, etale homotopy theory. See:

Čech Theory: Its Past, Present and Future https://doi.org/10.1216/RMJ-1980-10-3-429

Dave

http://alpha.math.uga.edu/~davide/