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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.
@article{TAC_2012_27_a5,
author = {Marino Gran and Zurab Janelidze and Diana Rodelo and Aldo Ursini},
title = {Symmetry of regular diamonds, the {Goursat} property, and subtractivity},
journal = {Theory and applications of categories},
pages = {80--96},
publisher = {mathdoc},
volume = {27},
year = {2012},
language = {en},
url = {http://geodesic.mathdoc.fr/item/TAC_2012_27_a5/}
}
TY - JOUR AU - Marino Gran AU - Zurab Janelidze AU - Diana Rodelo AU - Aldo Ursini TI - Symmetry of regular diamonds, the Goursat property, and subtractivity JO - Theory and applications of categories PY - 2012 SP - 80 EP - 96 VL - 27 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TAC_2012_27_a5/ LA - en ID - TAC_2012_27_a5 ER -
%0 Journal Article %A Marino Gran %A Zurab Janelidze %A Diana Rodelo %A Aldo Ursini %T Symmetry of regular diamonds, the Goursat property, and subtractivity %J Theory and applications of categories %D 2012 %P 80-96 %V 27 %I mathdoc %U http://geodesic.mathdoc.fr/item/TAC_2012_27_a5/ %G en %F TAC_2012_27_a5
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/