A morphism is not a binary relation. In a preorder, \\(\le\\) is a binary relation: for any pair of elements \\(x\\) and \\(y\\), \\(x \le y\\) is either true for false. When \\(x \le y\\) we can say there's a exactly one morphism from \\(x\\) to \\(y\\), if we so desire. But in a general category, there could be many (or no) morphisms \\(f : x \to y\\).

My remarks on morphisms were aimed only at people who know a bit of category theory and wonder why we're talking about preorders instead. So, if that stuff - or what I just said - makes no sense, don't worry about it too much.

My remarks on morphisms were aimed only at people who know a bit of category theory and wonder why we're talking about preorders instead. So, if that stuff - or what I just said - makes no sense, don't worry about it too much.