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 another category , in that we have a faithful functor , then given any object , its underlying object of is .
Last revised on June 26, 2024 at 06:36:58. See the history of this page for a list of all contributions to it.