Geodesic
Symmetry of regular diamonds, the Goursat property, and subtractivity
Theory and applications of categories, CT2011, Tome 27 (2012), pp. 80-96.

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We investigate $3$-permutability, in the sense of universal algebra, in an abstract categorical setting which unifies the pointed and the non-pointed contexts in categorical algebra. This leads to a unified treatment of regular subtractive categories and of regular Goursat categories, as well as of $E$-subtractive varieties (where $E$ is the set of constants in a variety) recently introduced by the fourth author. As an application, we show that ``ideals'' coincide with ``clots'' in any regular subtractive category, which can be considered as a pointed analogue of a known result for regular Goursat categories.
Publié le :
Classification : 18D99, 18C99, 18C05, 08B05
Keywords: Ideal of null morphisms, Goursat category, $3$-permutable variety, subtractive category, subtractive variety, ideal, clot, ideal determined category, good theory of ideals 
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     title = {Symmetry of regular diamonds, the {Goursat} property, and subtractivity},
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Marino Gran; Zurab Janelidze; Diana Rodelo; Aldo Ursini. Symmetry of regular diamonds, the Goursat property, and subtractivity. Theory and applications of categories, CT2011, Tome 27 (2012), pp. 80-96. http://geodesic.mathdoc.fr/item/TAC_2012_27_a5/