  Quotients and comprehension are fundamental mathematical constructions that
can be described via adjunctions in categorical logic. This paper reveals that
quotients and comprehension are related to measurement, not only in quantum
logic, but also in probabilistic and classical logic. This relation is
presented by a long series of examples, some of them easy, and some also highly
non-trivial (esp. for von Neumann algebras). We have not yet identified a
unifying theory. Nevertheless, the paper contributes towards such a theory by
introducing the new quotient-and-comprehension perspective on measurement
instruments, and by describing the examples on which such a theory should be
built.
