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.
Theory and Applications of Categories, Vol. 7, 2000, No. 2, pp 23-37 http://www.tac.mta.ca/tac/volumes/7/n2/n2.dvi http://www.tac.mta.ca/tac/volumes/7/n2/n2.ps ftp://ftp.tac.mta.ca/pub/tac/html/volumes/7/n2/n2.dvi ftp://ftp.tac.mta.ca/pub/tac/html/volumes/7/n2/n2.psTAC Home