  We prove standard results of group cohomology -- namely, existence of a long
exact sequence, classification of torsors via the first cohomology group,
Shapiro's lemma, the Hochschild-Serre spectral sequence, a decomposition of the
cochain complex in the direct product case, and Jannsen's result on the
recovery problem -- for cohomology theories such as continuous, analytic,
bounded, and pro-analytic cohomology. We also prove these results for certain
monoids. The cohomology groups considered here all have very concrete
interpretations by means of a cochain complex. Therefore, we do not use methods
of homological algebra, but explicit calculations on the level of cochains,
using techniques dating back to Hochschild and Serre.
