Forgetful Functor

A forgetful functorepresentr is a functor, typically a set-valued functor, which maps mathematical structures of a given type to their underlying sets. There are generally [[Adjoint Functor|adjoint functors]] with free functors.

Examples of Forgetful Functors

There are many simple examples of forgetful functors:

1. The forgetful functor from \(\text{Grp}\) to \(\text{Set}\) which maps a group to its underlying set.
2. The forgetful functor from \(\text{Top}\) to \(\text{Set}\) which maps a topological space to its underlying set.
3. The forgetful functor from the category of fields to the category of sets, which maps a field to its underlying set.