Separation of clones of cooperations by cohyperidentities

An nn-ary cooperation is a mapping from a nonempty set AA to the nnth copower of AA. A clone of cooperations is a set of cooperations which is closed under superposition and contains all injections. Coalgebras are pairs consisting of a set and a set of cooperations defined on this set. We define terms for coalgebras, coidentities and cohyperidentities. These concepts will be applied to give a new solution of the completeness problem for clones of cooperations defined on a two-element set and to separate clones of cooperations by coidentities.