We make a naive distinction between small and large collections, and implicitly use some intuitively plausible principles (for example, that any subcollection of a small collection is small). A category $ \mathscr{A} $ is small if the class or collection of all maps in $ \mathscr{A} $ is small, and large otherwise. If $ \mathscr{A} $ is small then the class of objects of $ \mathscr{A} $ is small too, since objects correspond one - to - one with identity maps.