How would one properly format a department/office/lab/subsection of a university? If say I work in Lab X of University Y, should I format it like this? Lab X, University Y or University Y, Lab X? Or something else?
In the context of describing affiliations of different authors on a paper "Department name, Faculty Name (optional), Institution name" is common. For example, see this paper: https://arxiv.org/pdf/1609.06958.pdf