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Condition Eq. (2.77) says precisely that we have a Galois connection in the sense of Definition 1.78. Let’s prove this fact. In particular, we’ll prove that a monoidal preorder is monoidal closed if, given any \( v \in V \), the map \( − \otimes v : V \rightarrow V \) given by multiplying with \(v\) has a right adjoint. We write this right adjoint \( v \multimap : V \rightarrow V \).