  We consider a U(2) Yang-Mills theory on M x S_F^2 where M is a Riemannian
manifold and S_F^2 is the fuzzy sphere. Using essentially the representation
theory of SU(2) we determine the most general SU(2)-equivariant gauge field on
M x S_F^2. This allows us to reduce the Yang-Mills theory on M x S_F^2 down to
an abelian Higgs-type model over M. Depending on the enforcement (or
non-enforcement) of a "constraint" term, the latter may (or may not) lead to
the standard critically-coupled abelian Higgs model in the commutative limit,
S_F^2 -> S^2. For M = R^2, we find that the abelian Higgs-type model admits
vortex solutions corresponding to instantons in the original Yang-Mills theory.
Vortices are in general no longer BPS, but may attract or repel according to
the values of parameters.
