  We provide a general technique for collectively analysing a manifestly
covariant formulation of non-abelian gauge theories on both anti de Sitter as
well as de Sitter spaces. This is done by stereographically projecting the
corresponding theories, defined on a flat Minkowski space, onto the surface of
the A(dS) hyperboloid. The gauge and matter fields in the two descriptions are
mapped by conformal Killing vectors and conformal Killing spinors,
respectively. A bilinear map connecting the spinors with the vector is
established. Different forms of gauge fixing conditions and their equivalence
are discussed. The U(1) axial anomaly as well as the non-abelian covariant and
consistent chiral anomalies on A(dS) space are obtained. Electric-magnetic
duality is demonstrated. The zero curvature limit is shown to yield consistent
findings.
