groups-as-eide hypothesis: a summary restatement

I have long suspected that:

  1. Identity: Groups are the forms in which the maximum of identity between terms and relations is realized.
  2. Ideality: This particular kind of identity is criterial for ideality, so that groups are eide.
  3. Plurality: Significantly, this maximal identity is only realized in each case of a concrete plurality of individual groups, not in a synthesis of all groups (DNE), and not by the concept of a group in general. (Groups behave more like Platonic ideas-forms than the post-Kantian Idea/Concept.) 
  4. Participation: A concept of participation seems to fall naturally out of this conception of groups, when we add relations to nongroups (as when we speak of the group of a space, etc.)