Saturated normal sub-IAPS

Definition
A sub-IAPS $$H$$ of an IAPS of groups $$(G,\Phi)$$ is termed a saturated normal sub-IAPS if it is saturated and normal. Equivalently, the quotient APS is an IAPS of groups.

The correct analogue of normal subgroup in the category of IAPSes is that of a saturated normal sub-IAPS, because the quotient APS is actually an IAPS of groups.