Since preorders don't guarantee antisymmetry, I'm a little concerned that meets and joins might not be unique. Is this a case in which category theory only concerns itself with "uniqueness up to isomorphism"? That seems reasonable enough at first, but it's at odds with phrases like "the meet" or "the join" and when considering the proof of Proposition 1.88, f, defined pointwise as a meet, doesn't seem like it's well-defined.