"A category is said to be small if its objects form a set."
Now one question is in my mind and that is although we know lots of sets and always working with them, but how we can show a class of objects form a set with proof. Some methods are easy and I know, like;
1- If we encounter to Countor contradiction we can say that our class of objects is not a set.
2- If we can earn our class of objects with getting union, intersection and some set operators from another well-known sets, by ZF axioms we can claim our class of objects is a set.
But I'm interest to have a method or definition if exists for use in all cases. If anybody knows more methods or even any other special cases, I will be glad to know.