Geodesic
Closedness properties of internal relations I: A unified approach to Mal'tsev, unital and subtractive categories
Theory and applications of categories, Tome 16 (2006), pp. 236-261.

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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.
Classification : 18C99, 08B05
Keywords: Mal'tsev, unital and subtractive category/variety, Jónsson-Tarski variety, term condition, internal relation 
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     author = {Zurab Janelidze},
     title = {Closedness properties of internal relations {I:}  {A} unified approach {to
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     journal = {Theory and applications of categories},
     pages = {236--261},
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     year = {2006},
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     url = {http://geodesic.mathdoc.fr/item/TAC_2006_16_a11/}
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Zurab Janelidze. Closedness properties of internal relations I:  A unified approach to
Mal'tsev, unital and subtractive categories. Theory and applications of categories, Tome 16 (2006), pp. 236-261. http://geodesic.mathdoc.fr/item/TAC_2006_16_a11/