These are unlike Wilkes' Media Dimensions. For any context within which collaboration operates, especially those in which various media are deployed to facilitate the collaboration, collaborative dimensions are the functions or tools available for working together.
For example, a wiki, such as Mediawiki, allows users to edit the same texts, to manage the editing process by through examining logs of changes, to comment on documents (and, thus, others' work), to exhibit personal information, etc. So-called content management systems, such as Drupal and Joomla, up the collaborative dimension ante considerably. They offer threading commenting, both RSS feeds and collectors, overt chronologically-based article access structures, multiple article types including book-like documents, editorial work flows, blogging functionality, etc.
Think also in terms of socializing systems, such as Facebook and Twitter. These are intrinsically snappy tools for sharing information and connecting with others. Blog tools are also pretty snappy on the information-sharing side and are maturing (of late) to encompass collaborative functionality in the more general-purpose content management system domain.