A monopoly right and a property right are the same thing with different names. As a landowner, for example, you have the right to kick people off (evict from) your property. You have both a de facto and de jure monopoly to exploit your land.
The US constitution confers to Congress the power to grant copyrights and patents in Article I, Section 8:
"The Congress shall have Power ... To promote the Progress of Science and useful Arts, by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries"
The operating word here is "exclusive" which, yes, is a monopoly right. But again, it's not different in essence from a property right, which is also a monopoly right.
The US constitution confers to Congress the power to grant copyrights and patents in Article I, Section 8:
"The Congress shall have Power ... To promote the Progress of Science and useful Arts, by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries"
The operating word here is "exclusive" which, yes, is a monopoly right. But again, it's not different in essence from a property right, which is also a monopoly right.