S-object

In algebraic topology, an formula_1-object (also called a symmetric sequence) is a sequence formula_2 of objects such that each formula_3 comes with an action of the symmetric group formula_4.
The category of combinatorial species is equivalent to the category of finite formula_1-sets (roughly because the permutation category is equivalent to the category of finite sets and bijections.)
formula_1-module.
By "formula_1-module", we mean an formula_1-object in the category formula_9 of finite-dimensional vector spaces over a field "k" of characteristic zero (the symmetric groups act from the right by convention). Then each formula_1-module determines a Schur functor on formula_9.