  The solution of quantum Yang-Mills theory on arbitrary compact two-manifolds
is well known. We bring this solution into a TQFT-like form and extend it to
include corners. Our formulation is based on an axiomatic system that we hope
is flexible enough to capture actual quantum field theories also in higher
dimensions. We motivate this axiomatic system from a formal
Schroedinger-Feynman quantization procedure. We also discuss the physical
meaning of unitarity, the concept of vacuum, (partial) Wilson loops and
non-orientable surfaces.
