John#5 Thanks! I believe I see the point your making.

Jacob#6 My understanding is that morphisms apply to objects, and categories consist of objects. It seems that in the case of a preorder, we have distinct elements, which may be objects, however, there is no transformation being done on them, they are merely 'put into some relation or equivalence'...the result of which can be a simple fact or ordering relation. When they are 'transformed', 'mapped', 'sent to', they are 'morphed'. I think \\( f(x) <= f(y) \\) could be a monomorphism if certain other conditions hold, but I admittedly know 0 category theory, so I'm just trying to understand the basic terminology as well, and I could certainly be mistaking things.