#
A Pseudo Representation Theorem for Various Categories of Relations

##
M. Winter

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.

Keywords: Relation Algebra, Dedekind category, Allegory, Representability, Matrix
Algebra.

2000 MSC: 18D10,18D15,03G15.

*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

http://www.tac.mta.ca/tac/volumes/7/n2/n2.pdf

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.ps

TAC Home