There is a micro-phenomenon of new wave, special snowflake directors that try to revolution the canons of classical opera. I saw Carmen being banged behind a burning car next to what looked like a flamenco-infused Thunderdome. That was in Paris opera, stronghold of modernist SJW nonsense.
Here, the expression is a shorter version of matriculation college. In a number of Canadian cities, many government-run secondary schools are called collegiates or collegiate institutes (C.I.), a complicated form of the word college which avoids the usual post-secondary connotation.
Intercollegiate is an adjective describing contests between schools. The NCAA is one specific body that some, but not all, colleges belong to, and which governs intercollegiate sports among its members. Division I is part of the NCAA. Other bodies which govern intercollegiate sports include the NAIA and others.