Editing Free object (section)

{{Short description|Left adjoint to a forgetful functor to sets}}
{{More citations needed|date=September 2024}}
In [[mathematics]], the idea of a '''free object''' is one of the basic concepts of [[abstract algebra]]. Informally, a free object over a [[Set (mathematics)|set]] ''A'' can be thought of as being a "generic" [[algebraic structure]] over ''A'': the only equations that hold between elements of the free object are those that follow from the defining axioms of the algebraic structure. Examples include [[free group]]s, [[tensor algebra]]s, or [[free lattice]]s.

The concept is a part of [[universal algebra]], in the sense that it relates to all types of algebraic structure (with [[finitary]] operations). It also has a formulation in terms of [[category theory]], although this is in yet more abstract terms.