Sentence:  In this chapter, we recall the definition of the category of \Sigma_-objects and we review the relationship between \Sigma_-objects and <WSD>functors</WSD>. In short, a \Sigma_-object (in English words, a symmetric sequence of objects, or simply a symmetric object) is the coefficient sequence of a generalized symmetric <WSD>functor</WSD> S(M) : X\rightarrow S(M,X), defined by a formula of the form / :: S(M,X) = \bigoplus^\infty_{r=0} \left ( M(r)\otimes X^{\otimes r}\right )_{\Sigma_r}. 
Meaning of the word marked with <WSD> tags:  A category homomorphism; a morphism from a source category to a target category which maps objects to objects and arrows to arrows, in such a way as to preserve domains and codomains (of the arrows) as well as composition and identities.