A RIDDL repository is an abstraction for anything that can retain information (e.g. messages) for retrieval at a later time. This might be a relational database, NoSQL database, a data lake, an API, or something not yet invented. There is no specific technology implied other than the retention and retrieval of information. You should think of repositories more like a message-oriented version of the Java Repository Pattern than any particular kind of database.
Repositories have traditionally had data schemas as part of their design definition; but RIDDL regards schemas as a technical detail of the implementation and leaves them unspecified. Repositories are only defined in terms of their message handling.
A repository has a handler that processes messages with respect to the repository’s stored information.
Command messages sent to the repository are updates to the repository. The handler should define how the update works and may optionally yield an Event message but generally that is handled at a higher level of abstraction.