Geodesic
On the Addition of Relations in an Abelian Category
Canadian journal of mathematics, Tome 22 (1970) no. 1, pp. 66-74

Voir la notice de l'article provenant de la source Cambridge University Press

In [1] the category of relations in an abelian category was studied. A relation from A to B appeared as an equivalence class of pairs of -morphisms (φ, ψ ), Moreover, this equivalence class may be written as the composite , where is canonically embedded in and is the image of Γ in the canonical involution on . Every equivalence class has an essentially unique minimal representative (φ 0,ψ 0), characterized by the property that where and if and only if the square is exact. 
Hilton, P. J.; Wu, Y.-C. On the Addition of Relations in an Abelian Category. Canadian journal of mathematics, Tome 22 (1970) no. 1, pp. 66-74. doi: 10.4153/CJM-1970-009-7
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[1] 1. Hilton, P. J., Correspondences and exact squares, Proc. Conf. Categorical Algebra (La Jolla, California, 1965), pp. 254–271 (Springer, New York, 1966). Google Scholar

[2] 2. Puppe, D., Korrespondenzen in Abelsche Kategorien, Math. Ann. 148 (1962), 1–30. Google Scholar

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