I am reading the 2008 book "Institution Independent Model Theory" by Razvan Diaconescu and looking up what the category ℂat was it states in the symbol Index
ℂat: the hyper-category of categories as objects and functors as arrows
But it nowhere defines what a hyper-category is. Is this just a way of saying that it is a Category containing Categories?
It's analogous to the idea of a "hyper-class," which is to classes what classes are to sets. Basically, in an appropriate background theory, a hypercategory consists of a hyperclass of objects and a hyperclass of morphisms, as opposed to a class of objects and a class of morphisms (= category) or a set of objects and a set of morphisms (= small category).
Note that to even talk about such things, we need to enrich our background set theory in a manner similar to how we move from ZFC to NBG. However, we can do this in a "conservative way," so this isn't as big a deal as it sounds.