On the decomposability of monadic algebras and automata

The structure connections between the endomorphisms, automorphisms, and all congruence relations of an arbitrary, not necessarily finite or strongly connected automaton are investigated. It is shown how the symmetries of an automaton carry over to symmetries of the lattice of congruence relations and to symmetries of quotient automata. A Galois connection is established between the endomorphisms and the congruence relations of an automaton.