Andrew Salch wrote:
let C be a class, and consider a family of subclasses C_i of C, which are indexed by an index class I. Am I allowed to take the intersection of a family of classes indexed by a class? Is the result a class?
Mike Shulman's answer is more comprhensive than what I could write, but I want to stress two points. For the first point, I quote Mike:
I think you *can* still define this intersection in MK, however
So there is a well-known theory of sets and classes in which you can do this. And the second point is that, unless you are particulary interested in the foundational and logical issues of size and categories, the first point is the only thing that you should care about. (Mike and I are interested in those issues, which is why he wrote a detailed answer and I was happy to read it. But "working" category theorists shouln't have to be.) --Toby [For admin and other information see: http://www.mta.ca/~cat-dist/ ]