A classification of universal algebras by infinitary relations

We will use the terminology and notation from [5]. Let A and E be nonempty sets and let A e be the set of all mappings from E into A. Any subset Q of A ~ will be called an E-relation or IEl-ary relation on A. I f ]El = k < N o we will identify E-relations with sets of ordered k-tuples of elements of A. Thus, if [El--2 the E-relations or 2-ary relations are simply the binary relations on A. If IEI = No we can identify E-relations with sets of sequences of elements of A. I f f i s an n-ary operation on A and gt,. . , g. ~Az thenfgt --.g. is the element o fA ~ defined by ( f g . . . . . g.) (e) = f ( g l (e) . . . . . g. (e)) for any e ~ E.