Bennett and Stinespring, Together at Last

We present a universal construction that relates reversible dynamics on open systems to arbitrary closed systems: the restriction affine completion of monoidal category quotiented by well-pointedness. This categorical encompasses both quantum channels, via Stinespring dilation, and classical computing, Bennett's method. Moreover, in these two cases, we show how our can be essentially 'undone' further construction. shows mixed theory computation rest entirely foundations.