A Pseudo Representation Theoremfor Various Categories of Relationsm

نویسندگان

  • M Winter
  • Andrew Pitts
چکیده

It is well-known that, given a Dedekind category R the category of (typed) matrices with coeecients from 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 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 R. Furthermore, we use our concept of a basis to extend a known result from the theory of heterogeneous relation algebras.

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تاریخ انتشار 2000