If you define the entity as “all institutions that are allowed to create and enforce laws” and then say “that entity has a monopoly on creating and enforcing la

If you define the entity as “all institutions that are allowed to create and enforce laws” and then say “that entity has a monopoly on creating and enforcing laws” you’ve created a tautology. There are clear counter examples to your statement in the U.S. States are not “allowed” to use violence because the Federal government says it’s okay. States have a right to create and enforce laws.