Editing Forgetful functor (section)

{{Short description|Concept in category theory}}
In [[mathematics]], more specifically in the area of [[category theory]], a '''forgetful functor''' (also known as a '''stripping functor''') "forgets" or drops some or all of the input's [[Mathematical structure|structure]] or [[Mathematical property|properties]] {{em|before}} [[Map (mathematics)|mapping]] to the output. For an [[algebraic structure]] of a given [[signature (logic)|signature]], this may be expressed by curtailing the signature: the new signature is an edited form of the old one. If the signature is left as an empty list, the [[functor]] is simply to take the [[Algebraic structure|underlying set]] of a structure. Because many structures in mathematics consist of a set with an additional added structure, a forgetful functor that maps to the underlying set is the most common case.