If you've defined the natural number 2 to be an arbitrary set with cardinality 2, you're including sets which contain the number 2. That's the basic form of Rus

If you've defined the natural number 2 to be an arbitrary set with cardinality 2, you're including sets which contain the number 2. That's the basic form of Russell's paradox. If you define the natural number 2 to be the category of pairs, your objects are the sets with cardinality 2, and your relations between objects are equivalence relations. As a consequence your category 2 will contain sets which contain itself.