Well, I've studied under a pupil of Grothendieck, so, yes inaccessible cardinals are at the heart of his category theory. When you study this long enough, you w

Well, I've studied under a pupil of Grothendieck, so, yes inaccessible cardinals are at the heart of his category theory. When you study this long enough, you will discover they essentially perform the function of what in computer science is the class concept (which why these structures were called 'universes'). But Russell already developed a type theory around 1900. Most mathematicians have never cared to really study Gödel for instance. Because you then would have to read Russell's principia mathematica and Frege's concept script.