  We describe the moduli space of extensions in the model category of
simplicial presheaves. This article can be seen as a generalization of
Blomgren-Chacholski results in the case of simplicial sets. Our description of
the moduli space of extensions treat the equivariant and the nonequivariant
case in the same setting. As a new result, we describe the moduli space of
M-bundles over a fixed space X, when M is a simplicial monoid. Moreover, the
moduli space of M-bundles is classified by the classifying space of the
simplicial submonoid generated by homotopy invertible elements of M. We give a
general interpretation of generalized cohomology theories (connective) in terms
of classification of principle bundles. We also construct categorical model for
the classifying space BG and EG when G is a simplicial (topological) monoid
group like.
