IAPS of groups
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This article gives a basic definition in the following area: APS theory
View other basic definitions in APS theory |View terms related to APS theory |View facts related to APS theory
This article defines the notion of group object in the category of IAPSs|View other types of group objects
An IAPS of groups is an IAPS over the category of groups. More specifically an IAPS is the following data:
- For each natural number , a group denoted
- For each ordered pair of natural numbers, an injective homomorphism
Satisfying the following compatibility conditions:
For in respectively:
The above condition is termed an associativity condition.
We may assume as the trivial group and define and as trivial paddings.
Note that if we remove the condition of injectivity, we get an APS of groups.
Further information: sub-IAPS of groups
Let be an IAPS of groups. A sub-IAPS associated to every a subgroup of such that the image of under lies inside . Note that this is the same as a sub-APS of groups because the injectivity condition comes for free.