Symmetric objects and functors

In this chapter, we recall the definition of the category of Σ∗-objects and we review the relationship between Σ∗-objects and functors. In short, a Σ∗-object (in English words, a symmetric sequence of objects, or simply a symmetric object ) is the coefficient sequence of a generalized symmetric functor S(M) : X→ S(M,X), defined by a formula of the form In §2.1, we recall the definition of the tensor product of Σ∗-objects, the operation which reflects the pointwise tensor product of functors and which provides the category of Σ∗-objects with the structure of a symmetric monoidal category over the base category.