Polynomial functor
In algebra, a polynomial functor is an endofunctor on the category V {\displaystyle {\mathcal {V}}} of finite-dimensional vector spaces that depends polynomially on vector spaces. For example, the symmetric powers V ↦ Sym n ( 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}}} ; these two are also Schur functors.