Given a concrete category, that is a category equipped with a functor from to the category of sets (satisfying certain conditions), we call a forgetful functor and call , for an object of , the underlying set of .
In the case where is explicitly a category of structured sets, then every object of is a set equipped with some extra structure. In that case, the underlying set of is precisely this set .
More generally, if is concrete over , so we have faithful, then given any object , its underlying object of is .
Revised on August 29, 2012 19:41:41
by Toby Bartels