What makes you think the Inquisition was a separate entity from the Catholic Church, as you seem to imply?
What is currently called the Congregation for the Doctrine of the Faith used to be called Congregation for Universal Inquisition (erected in 1542), which changed its name to Congregation of the Holy Office in 1908.
Also, a good book on the Inquisition, which dispels the myth that the Catholic Church executed people (it was the State who actually did that), is canon lawyer Ed Peters's Inquisition. There's also a good Old Catholic Encyclopedia article "Inquisition."