The structure of isomorphisms of universal hypergraphical automata

Universal hypergraphical automata are universally attracted objects in the category of automata, for which the set of states and the set of output symbols are equipped with structures of hypergraphs. It was proved earlier that a wide class of such sort of automata are determined up to isomorphism by their semigroups of input symbols. We investigate a connection between isomorphisms of universal hypergraphical automata and isomorphisms of their components: semigroups of input symbols and hypergraphs of states and output symbols.