When is a map essential in Čech cohomology?

Solution 1:

Hillas has an excellent working paper where you can get a nice intuition of what such an essentiality condition implies. The title is "A Game Illustrating Some Features of the Definition of Strategic Stability".

Solution 2:

I found the paper where a correct definition of essentiality is given:

Srihari Govindan and Jean-Francois Mertens (1993): \An Equivalent Def- inition of Stable Equilibria"

If you want I will send it by e-mail. As to Cech cohomology, there is the classical book

Spanier, Ediwin H (1966) Algebraic Topology. McGraw Hill, New York.

However it is very thick. I can recommend, e.g.,

Morgan J. W., Lamberson P. J. Algebraic Topology

(I can send it also; though I didn't read it).