  It is shown that every algebraic quantum field theory has an underlying
functorial field theory which is defined on a suitable globally hyperbolic
Lorentzian bordism pseudo-category. This means that globally hyperbolic
Lorentzian bordisms between Cauchy surfaces arise naturally in the context of
algebraic quantum field theory. The underlying functorial field theory encodes
the time evolution of the original theory, but not its spatially local
structure. As an illustrative application of these results, the algebraic and
functorial descriptions of a free scalar quantum field are compared in detail.
