We study closedness properties of internal relations in finitely complete categories, which leads to developing a unified approach to: Mal'tsev categories, in the sense of A. Carboni, J. Lambek and M. C. Pedicchio, that generalize Mal'tsev varieties of universal algebras; unital categories, in the sense of D. Bourn, that generalize pointed Jónsson-Tarski varieties; and subtractive categories, introduced by the author, that generalize pointed subtractive varieties in the sense of A. Ursini.
Keywords: Mal'tsev, unital and subtractive category/variety; Jónsson-Tarski variety; term condition; internal relation
2000 MSC: 18C99, 08B05
Theory and Applications of Categories,
Vol. 16, 2006,
No. 12, pp 236-261.