The following three conclusions are found: (1) By regular order-sorted theory morphism being deduced to many-sorted theory morphism, both model functors ( )·and ( )# being commutative with φ have been proved; (2) Lawvere theorem in Institution of regular order-sorted equational logic is presented; (3) The correspondence among initial (terminal) semantics of glued theories and factor theories in Institution of regular order-sorted equational logic is clarified.