For example if a crime is committed inside the university campus, Could the police get inside the university without a warrant or they have to ask for permission to go inside?
How does that work for private or public universities?
Many citizens disagree as to why tye are untouchables if lets say a social crim
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In my country we exclusively have public universities. No private ones.
And no, they are not autonomous in the sense of private, independent entities. They are public ground... basically like a library, museum, public bath, park etc. If a crime were to happen, the police wouldn't need a warrant to search classrooms, office space, the cafeterias etc. The universities also tend to work closely together with the police and justice system. For example if you are caught doing plagiarism, the head of your department will directly report you to the police and file a lawsuit. Universities only have autonomy when it comes to academia itself. For example in the case of plagiarism, the head of your department would kick you out of your field of study and possibly out of the university as a whole. Anything that goes beyond this does not lie within the power of university staff/officials (and they are not allowed to obstruct the justice system in any way).
Also, since they are public universities, literally anyone can visit/attend them. For example you could travel to Switzerland as a tourist and sit into a lecture held in English. Nobody would question you. In fact, we have quite a lot of senior citizens who aren't officially enrolled in any study program and maybe don't have the qualifications to enrol in an university but still visit lectures from time to time simply because they're interested and want to learn something.
In private universities abroad, this is not necessarily the case. For example last summer my wife and I visited Boston and thus went to see Harvard. We really wanted to have a look at the beautiful library from inside but were quite shocked to find out that you can only enter it if you are enrolled at Harvard and you can show your student ID. There was even a guard. We weren't used to that from Switzerland.