> Actually, I don't think that the answer that was given is right.

The enrichment doesn't give us any information about how objects are related, so we can only really get a set, as Anindya points out -- and there's a trivial information-free preorder, the codiscrete preorder, which we can endow on any set. Can you explain where this logic falls through?

**EDIT:** changed "discrete" to "codiscrete" -- all arrows need to be the same, but the discrete preorder has "existing" identity arrows and "nonexistent" other arrows. The codiscrete preorder has all arrows.

The enrichment doesn't give us any information about how objects are related, so we can only really get a set, as Anindya points out -- and there's a trivial information-free preorder, the codiscrete preorder, which we can endow on any set. Can you explain where this logic falls through?

**EDIT:** changed "discrete" to "codiscrete" -- all arrows need to be the same, but the discrete preorder has "existing" identity arrows and "nonexistent" other arrows. The codiscrete preorder has all arrows.