In algebra, a polynomial functor is a functor on the category V{\displaystyle {\mathcal {V}}} of finite-dimensional vector spaces that depends polynomially on vector spaces. For example, the symmetric powers V↦Symn⁡(V){\displaystyle V\mapsto \operatorname {Sym} ^{n}(V)} and the exterior powers V↦∧n(V){\displaystyle V\mapsto \wedge ^{n}(V)} are polynomial functors from V{\displaystyle {\mathcal {V}}} to V{\displaystyle {\mathcal {V}}} .