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Points of affine categories and additivity
A. Carboni and G. Janelidze, 127-131
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.
A. Carboni and G. Janelidze, 127-131
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.
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