On exponentiation of universal hyperalgebras

Abstract.

For universal hyperalgebras we study a binary operation of exponentiation which to a pair of universal hyperalgebras of a given type assigns their power, i.e., a universal hyperalgebra of the same type carried by the corresponding set of homomorphisms. We give sufficient conditions for the existence of such a power and for a decent behaviour of the exponentiation. As a consequence of our investigations we discover a cartesian closed subcategory of the category of universal hyperalgebras of the same type and homomorphisms between them.