Now by "the cathedral" Yarvin means a lot more than just higher education institutes, he's talking about what you or I might call the larger liberal establishment here; the universities, the publishing houses, the media, etc
I don't want to spend a lot of time explaining this absolute fuckhead's grand strategies, you can find analysis online - but the basic idea is to destroy, or seize control of any institution that isn't willing to push fascist propaganda and support this neo-Monarchal order