Proposition 1.81 (the basic theory of Galois connections) starts by supposing
that \\(f: P → Q\\) and \\(g: Q → P\\) are functions and shows that two things
are equivalent: a.) is that \\(f\\) and \\(g\\) form a Galois connection and b.)
is Eq. (1.6). Going from a.) to b.) is straightforward. In the proof of the
reverse, from b.) to a.), the first step in the proof goes: "then since \\(g\\)
is monotonic...". Is this a valid assumption? This is the first step is this
side of the proof and the basic setup only invites us to suppose that \\(f: P →
Q\\) and \\(g: Q → P\\) are functions.