The questions around Collaboration Management Platform interoperation

What needs to be shared between diverse CMP to have them interoperate? What specific attributes or metadata must be shared (if anything) for different CMP platforms to converse? What are the anchor identifiers?

Grouper Group sync as an example/use case

https://spaces.at.internet2.edu/display/Grouper/Syncing+groups+between+group+management+systems

Shibboleth as an example/use case