Question: Columbia University and Wake Forest University, are which type of mutual university?
Context: Edwin Graves Wilson (born February 1, 1923) is a professor at Wake Forest University.  His professional academic and administrative tenure at Wake Forest spanned from 1951 until his retirement in 1993.  He is referred to affectionately by members of the Wake Forest community as "Mr. Wake Forest."  He is a 1943 graduate of Wake Forest with a Bachelor of Arts degree in English. The Wake Forest University Demon Deacons women's soccer team is an amateur, NCAA Division I college soccer team composed of students attending Wake Forest University in Winston-Salem, North Carolina.  They achieved their greatest result in 2011, when they reached the College Cup.  Like all sports teams from Wake Forest, women's soccer competes in the Atlantic Coast Conference.  The Deacons play their home matches at Spry Stadium on the campus of Wake Forest. Wake Forest School of Medicine is the medical school of Wake Forest University, located in Winston-Salem, North Carolina.  It is affiliated with Wake Forest Baptist Medical Center, the academic medical center whose clinical arm is Wake Forest Baptist Health.  "U.S. News & World Report" in 2015 ranked Wake Forest School of Medicine as 49th best for research in the nation and 71st best for primary care.  The School of Medicine also ranks in the top third of U.S. medical schools in funding from the National Institutes of Health (NIH). The Wake Forest University Demon Deacons men's soccer team is an amateur, NCAA Division I college soccer team composed of students attending Wake Forest University in Winston-Salem, North Carolina.  They achieved their greatest result in 2007, winning the 2007 Division I Men's College Cup.  Like all sports teams from Wake Forest, men's soccer competes in the Atlantic Coast Conference (ACC).  The Deacons play their home matches at Spry Stadium on the campus of Wake Forest. The North Carolina–Wake Forest rivalry is a series of athletic contests between in-state rivals, the University of North Carolina Tar Heels and the Wake Forest University Demon Deacons.  The first game was played in 1888 between the two institutions.  Wake Forest was originally located in Wake Forest, North Carolina until it moved its campus across the state of North Carolina to Winston-Salem, North Carolina in 1956.  Since ACC expansion the two schools cannot play the yearly rivalry due to scheduling and being in separate divisions.  UNC is a Coastal Division member and Wake Forest, an Atlantic Division member respectively. The Wake Forest University School of Law is one of the professional graduate schools of Wake Forest University.  Located in Winston-Salem, North Carolina, Wake Forest University School of Law is a private American Bar Association (ABA) accredited law school and is a member of the Association of American Law Schools (AALS).  The school was established in 1894.  U.S. News & World Report consistently ranks the school among the Top Tier Law Schools in the nation.  The current dean is Suzanne Reynolds. Wake Forest University is a private, independent, nonprofit, nonsectarian, coeducational research university in Winston-Salem, North Carolina, founded in 1834.  The university received its name from its original location in Wake Forest, north of Raleigh, North Carolina, the state capital.  The Reynolda Campus, the university's main campus, has been located north of downtown Winston-Salem since the university moved there in 1956.  The Wake Forest Baptist Medical Center campus has two locations, the older one located near the Ardmore neighborhood in central Winston-Salem, and the newer campus at Wake Forest Innovation Quarter downtown.  The university also occupies lab space at Biotech Plaza at Innovation Quarter, and at the Center for Nanotechnology and Molecular Materials.  The University's Graduate School of Management maintains a presence on the main campus in Winston-Salem and in Charlotte, North Carolina. Wake Forest Innovation Quarter in Winston-Salem, North Carolina, is an innovation district focused on research, business and education in biomedical science, information technology, digital media, clinical services and advanced materials.  The Innovation Quarter, operated by Wake Forest Baptist Medical Center, is home to academic groups, private companies and other organizations located on 330 acres in downtown Winston-Salem.  Its tenants include departments from five academic institutions—Wake Forest School of Medicine, Wake Forest University, Forsyth Technical Community College, Winston-Salem State University, UNC School of the Arts— as well as private businesses and other organizations.  One tenant is the Wake Forest Institute for Regenerative Medicine (WFIRM), which is working to engineer more than 30 different replacement tissues and organs and to develop healing cell therapies.  The science and research conducted at WFIRM is behind two start-up companies at Innovation Quarter.  The ability of researchers and scientists to work alongside entrepreneurs furthers a goal of Innovation Quarter to develop new treatments and cures for disease and advances in technology. Columbia University (Columbia; officially Columbia University in the City of New York), established in 1754, is a private Ivy League research university in Upper Manhattan, New York City, often cited as one of the world's most prestigious universities. Groves Stadium, currently known as Trentini Stadium, is a stadium in Wake Forest, North Carolina, United States.  It hosted the Wake Forest University Demon Deacons football team until the school moved to Winston-Salem, North Carolina and Bowman Gray Stadium.  Since then, the stadium has hosted the homes games of Wake Forest High School.  The stadium held 20,000 people at its peak and was opened in 1940.  It is currently named after former Wake Forest University player and coach of Wake Forest-Rolesville High School, Tony Trentini.  Wake Forest University's current home stadium was also known as Groves Stadium until 2006.
Answer: private