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.

http://www.tac.mta.ca/tac/volumes/16/6/16-06.dvi

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http://www.tac.mta.ca/tac/volumes/16/6/16-06.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/16/6/16-06.dvi

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/16/6/16-06.ps