Editing Free object (section)

===General case===
Other types of forgetfulness also give rise to objects quite like free objects, in that they are left adjoint to a forgetful functor, not necessarily to sets.

For example, the [[tensor algebra]] construction on a [[vector space]] is the left adjoint to the functor on [[associative algebra]]s that ignores the algebra structure. It is therefore often also called a [[free algebra]]. Likewise the [[symmetric algebra]] and [[exterior algebra]] are free symmetric and anti-symmetric algebras on a vector space.