I am not sure if I do use the association and aggregation or composition diamond properly.
I would use the Association for interfaces, because I can\'t instantiate
Let's set the terms. The Aggregation is a metaterm in the UML standard, and means BOTH composition and shared aggregation, simply named shared. Too often it is named incorrectly "aggregation". It is BAD, for composition is an aggregation, too. As I understand, you mean "shared".
Further from UML standard:
composite - Indicates that the property is aggregated compositely, i.e., the composite object has responsibility for the existence and storage of the composed objects (parts).
So, University to cathedras association is a composition, because cathedra doesn't exist out of University (IMHO)
Precise semantics of shared aggregation varies by application area and modeler.
I.e., all other associations can be drawn as shared aggregations, if you are only following to some principles of yours or of somebody else. Also look here.