Geodesic
A Pseudo Representation Theorem for Various Categories of Relations
Theory and applications of categories, Tome 7 (2000), pp. 23-37

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

It is well-known that, given a Dedekind category {\cal R} the category of (typed) matrices with coefficients from {\cal R} is a Dedekind category with arbitrary relational sums. In this paper we show that under slightly stronger assumptions the converse is also true. Every atomic Dedekind category {\cal R} with relational sums and subobjects is equivalent to a category of matrices over a suitable basis. This basis is the full proper subcategory induced by the integral objects of {\cal R}. Furthermore, we use our concept of a basis to extend a known result from the theory of heterogeneous relation algebras.

Classification : 18D10, 18D15, 03G15.
Keywords: Relation Algebra, Dedekind category, Allegory, Representability, Matrix Algebra. 
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     author = {M. Winter},
     title = {A {Pseudo} {Representation} {Theorem} for {Various} {Categories} of {Relations}},
     journal = {Theory and applications of categories},
     pages = {23--37},
     publisher = {mathdoc},
     volume = {7},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2000_7_a1/}
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M. Winter. A Pseudo Representation Theorem for Various Categories of Relations. Theory and applications of categories, Tome 7 (2000), pp. 23-37. http://geodesic.mathdoc.fr/item/TAC_2000_7_a1/