In algebraic topology, an -object (also called a symmetric sequence) is a sequence of objects such that each comes with an action [note 1] of the symmetric group .
The category of combinatorial species is equivalent to the category of finite -sets (roughly because the permutation category is equivalent to the category of finite sets and bijections.) [1]
By -module, we mean an -object in the category of finite-dimensional vector spaces over a field k of characteristic zero (the symmetric groups act from the right by convention). 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.