The Citadel is a college, not a university or school. When referring to the institution as a college, the word should be lowercased. Even when referring specifically to The Citadel, do not capitalize. Treat the word “college” like any other noun that is not a proper name.
There are five schools in the college—the Tommy and Victoria Baker School of Business, the Zucker Family School of Education, the School of Engineering, the School of Humanities and Social Sciences, and the Swain Family School of Science and Mathematics.