Definition 1.55 includes this sentence: "A monotone function \\(f: P \to Q\\) is called an *isomorphism* if there exists a monotone function \\(g: Q \to P\\) such that \\(f.g = id_P\\) and \\(g.f = id_Q\\).” (Here \\(P\\) and \\(Q\\) are preorders each with its own ordering).

Question: Is the “and…” part redundant? It seems that \\(g.f = id_Q\\) is implied by what precedes it.

Question: Is the “and…” part redundant? It seems that \\(g.f = id_Q\\) is implied by what precedes it.