  We quantize abelian Yang-Mills theory on Riemannian manifolds with boundaries
in any dimension. The quantization proceeds in two steps. First, the classical
theory is encoded into an axiomatic form describing solution spaces associated
to manifolds. Second, the quantum theory is constructed from the classical
axiomatic data in a functorial manner. The target is general boundary quantum
field theory, a TQFT-type axiomatic formulation of quantum field theory.
