Carboni, A.; Janelidze, G. Points of affine categories and additivity. (English) Zbl 1088.18005 Theory Appl. Categ. 16, 127-131 (2006). Let \(\mathcal C\) be a pointed category with finite limits and finite coproducts. For any object \(B\) in \(\mathcal C\), let \({\mathcal P} t({\mathcal C}, B)\) be the category of pointed objects in the comma category \(({\mathcal C}, B)\), and let \(F_B: {\mathcal C}\to{\mathcal P} t({\mathcal C}, B)\) be the functor defined by \(F_B(X)= (B+ X, (1,0), i_1)\). In this paper, it is proved that the category \(\mathcal C\) is additive if and only if it has a class \(S\) of (adequately defined) generators \(B\) such that the functors \(F_B: {\mathcal C}\to \mathcal P t({\mathcal C}, B)\) are equivalences of categories. Reviewer: Yves Diers (Faches-Thumesnil) MSC: 18C05 Equational categories 18C10 Theories (e.g., algebraic theories), structure, and semantics 18C20 Eilenberg-Moore and Kleisli constructions for monads Keywords:additive category; pointed object; algebraic category; affine spaces PDFBibTeX XMLCite \textit{A. Carboni} and \textit{G. Janelidze}, Theory Appl. Categ. 16, 127--131 (2006; Zbl 1088.18005) Full Text: EuDML EMIS