Other types of forgetfulness also give rise to objects quite like free objects: for example the tensor algebra construction on a vector space as left adjoint to the functor on associative algebras that ignores the algebra structure.
Other types of forgetfulness also give rise to objects quite like free objects: for example the tensor algebra construction on a vector space as left adjoint to the functor on associative algebras. This vector space as left adjoint to the functor on associative algebras ignores the algebra structure.