Let $C$ be a category and $C/R$ its quotient category.
According to Wikipedia:
There is a natural quotient functor from C to C/R which sends each morphism to its equivalence class. This functor is bijective on objects and surjective on Hom-sets (i.e. it is a full functor).
Question: Notice the bolded above; why doesn't Wikipedia just state that this functor is the identity mapping on objects? Is it ever not the identity mapping (on objects)?