TITLE: When is a map essential in Čech cohomology?
QUESTION [12 upvotes]: I read a nice survey of parts of game theory, Foundations of Strategic Equilibrium, by Hillas and Kohlberg. Something where I stumble is the discussion of Mertens stability. There is a definition that requires a certain map to be essential in Čech cohomology and I know nothing about cohomology. So I would like to know:

Is there a self-contained way to define essentiality of a map in Čech
  cohomology that can be explained to someone who knows point-set
  topology quite well but knows almost nothing about algebraic topology?
  If yes, please give the definition and maybe a bit of explanation..

REPLY [3 votes]: 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".