Normal sub-APS

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This term is related to: APS theory
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ANALOGY: This is an analogue in APS of a property encountered in group. Specifically, it is a sub-APS property analogous to the subgroup property: normal subgroup
View other analogues of normal subgroup | View other analogues in APSs of subgroup properties (OR, View as a tabulated list)

Definition

Let $(G,\Phi )$ be an APS of groups and $H$ be a sub-APS of $G$ . We say that $H$ is normal in $G$ if the following equivalent conditions hold:

For every $n$ , $H_{n}$ is a normal subgroup of $G_{n}$
There exists an APS of groups $(K,\Psi )$ and an APS homomorphism from $(G,\Phi )$ to $(K,\Psi )$ such that the kernel of the map at each $n$ is $H_{n}$