A BPMN diagram is used for visualizing BPMN collaboration and BPMN processes. The diagram can have any type of elements and is not assigned to a special element.
A process does not only exist for itself; it is normally also to be seen in a certain context. If the process is used or called by another process, it should be able to be shown within that call activity. If the process is called by a participant of a collaboration, it should be able to be shown within the participant. If the process is derived from other model elements or is used as the basis for derivation of another element, it should be able to be shown together with the other elements.
Each visualization may be important for different aspects of the process. Not necessarily every task of a process is relevant in a collaboration and for its participants. If the modeler is interested in communication between those involved, they may only want those elements relevant to communication in the process shown and want to hide the objects, including their data associations.
This means that the process needs to be visualized many times and adjusted to suit the context.
This answer is not so obvious for a collaboration: Whereas the process can occur in various collaborations and, for this reason alone, needs to be able to be used more than once, it is not like this for collaborations. You cannot call them at the same time or use them within other BPMN elements.
However, a collaboration can be viewed with various aims in mind. This enables each view to focus on a certain participant and hide the information which just concerns the other participant or person working on the project. This means you can show the collaboration from the perspective of the initiator but also from the perspective of the reactive person involved in the project. You do not need to do this but Innovator is not going to put obstacles in your way.
That ties in with the concept of the whiteboard diagram. You do not need to look at the BPMN diagram itself next to the whiteboard diagram - but the fact that you can is an important step when making models in their entirety easier to understand:
It allows you to put a BPMN diagram next to a structure diagram and show the links between process elements and structures.
It allows you to put a diagram next to a structure diagram and show the links between objects and object structures.
It allows you to put the diagram next to an org chart to show what the organizational entities' structure looks like which you have used for the process' lanes and the task's activity resources.
It allows you to show dependencies and mapping relationships between BPMN elements in a diagram and any other number of model elements, be it UML classes, UML use cases or database tables.
To make a whiteboard diagram as simple as possible, you shouldn't show everything all at the same time - a BPMN diagram would appear more than once, after all!
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