A cartesian restriction category is equivalently a copy-discard category where all morphisms are deterministic. This is Cockett Lack (2013), Theorem 5.2. References. Restriction Categories III, Colimits, Partial Limits and Extensivity (Cockett, Lack, 2013) Partiality, Cartesian Closedness and Toposes (Curien, Obtułowicz, 1989)