TITLE: Can skeleta simplify category theory?
QUESTION [27 upvotes]: I am not by any means an expert in category theory. Anyway whenever I have studied a concept in category theory I have always had the feeling that most of the subtleties introduced are artificial.
For a few examples:
-one does not usually consider isomorphic, but rather equivalent categories
-universal objects are unique only up to a canonical isomorphism
-the category of categories is really a 2-category, so some natural constructions do not yield functors into categories, but only pseudofunctors
-cleavages of fibered categories do not always split
....
My question is: can skeleta be used to simplify all this stuff? It looks like building everything using skeleta from the beginning would remove a lot of indeterminacies in these constructions. On the other hand it may be the case that this subtleties are really intrinsic, and so using skeleta, which are not canonically determined, would only move the difficulties around.

REPLY [6 votes]: While I agree with the above answers, I know of some situations where it might be good to take a skeleton (or something like it). This has to do with large categories which are essentially small. You might want to take a skeleton or at least a a small category that is equivalent to the original, so as to avoid size problems.