A category C is additive if and only if, for every object B of C, the category Pt(C,B) of pointed objects in the comma category (C,B) is canonically equivalent to C. We reformulate the proof of this known result in order to obtain a stronger one that uses not all objects of B of C, but only a conveniently defined generating class S. If C is a variety of universal algebras, then one can take S to be the class consisting of any single free algebra on a non-empty set.
Keywords: Algebraic categories, affine spaces
2000 MSC: 18C05, 18C10, 18C20
Theory and Applications of Categories,
Vol. 16, 2006,
No. 6, pp 127-131.