S-object

In algebraic topology, an -object is a sequence of objects such that each comes with an action of the symmetric group.
The category of combinatorial species is equivalent to the category of finite -sets

S-module

By -module, we mean an -object in the category of finite-dimensional vector spaces over a field k of characteristic zero. Then each -module determines a Schur functor on.
This definition of -module shares its name with the considerably better-known model for highly structured ring spectra due to Elmendorf, Kriz, Mandell and May.