Original Post

Everything is great about Univalent Foundations and Category Theory until you give a deep thought to things like A&~A denial, axiom of choice rejection, intuitionist logic (and its school and branding "nihilistic" consequences), and to the very constructive "foundations" as their denial of classicality.

Just saying. There's a "holy war" surrounding this. There's other point of view, greatly argumented by Putnam in 1960s. Fundamentalism is a famous thing in religion, too...