We introduce a notion of a subtractive category. It generalizes the notion of a pointed subtractive variety of universal algebras in the sense of A. Ursini. Subtractive categories are closely related to Mal’tsev and additive categories: (i) a category C with finite limits is a Mal’tsev category if and only if for every object X in C the category Pt(X)=((X,1X)↓(C↓X)) of “points over X” is subtractive; (ii) a pointed category C with finite limits is additive if and only if C is subtractive and half-additive.
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