How about the category of sets with injective maps as morphisms? As an ad hoc example, this may not count as "natural", but it's simple enough.
[EDIT] following Martin's comment: take the dual, or replace "injective" by "surjective".
How about the category of sets with injective maps as morphisms? As an ad hoc example, this may not count as "natural", but it's simple enough.
[EDIT] following Martin's comment: take the dual, or replace "injective" by "surjective".