Algebras of co-relations on a finite set (Q2759845)

An \(n\)-ary co-operation on a set \(X\) is a map from \(X\) to its \(n\)-th co-power, \(\{1,2,\dots,n\}\times X\) and an \(\alpha\)-ary co-relation on \(X\) is a subset of \(\alpha^X\), where \(\alpha\) is an ordinal. Operations, some of which are somewhat unintuitive, are defined on the set of co-relations, leading to various types of algebras. The authors pause to justify these choices, pointing out that in certain situations (such as the study of Kleene algebras of regular languages) algebras of co-relations seem more useful than algebras of relations. The final section uses special co-relations in the study of properties of clones of co-operations.NEWLINENEWLINEFor the entire collection see [Zbl 0970.00014].