  The treatment of the principle of general covariance based on coordinate
systems, i.e., on classical tensor analysis suffers from an ambiguity. A more
preferable formulation of the principle is based on modern differential
geometry: the formulation is coordinate-free. Then the principle may be called
``principle of geometricity.'' In relation to coordinate transformations, there
had been confusions around such concepts as symmetry, covariance, invariance,
and gauge transformations. Clarity has been achieved on the basis of a
group-theoretical approach and the distinction between absolute and dynamical
objects. In this paper, we start from arguments based on structures on
cosmological manifold rather than from group-theoretical ones, and introduce
the notion of setting elements. The latter create a scene on which dynamics is
performed. The characteristics of the scene and dynamical structures on it are
considered.
