Quadratic endofunctors of the category of groups
Quadratic and more generally polynomial endofunctors have been studied in the literature for additive categories, in particular for the category of abelian groups [\textit{S. Eilenberg} and \textit{S. MacLane}, Ann. Math., II. Ser. 60, 49-139 (1954; Zbl 0055.41704)] and for categories of vector spaces over suitable fields. Polynomial endofunctors of the category of topological spaces have been examined by \textit{T. Goodwillie} [K-Theory 4, No. 1, 1-27 (1990; Zbl 0741.57021); ibid. 5, No. 4, 295-332 (1992; Zbl 0776.55008)]. The purpose of the paper under review is to study quadratic endofunctors on the category of groups. A possible motivation is the observation that polynomial endofunctors of the category of groups applied to simplicial groups yield polynomial endofunctors for spaces. The main result of the paper says that the monoidal category of (suitably defined) quadratic endofunctors of the category of groups is equivalent to the monoidal category of square groups, the notion of square group being defined as a diagram of three groups with appropriate properties.
scientific article; zbMATH DE number 1251312
scientific article