Definition of $\mathscr{U}$-small set

Question

Let $\mathscr{U}$ be a Grothendieck Universe. Then Kashiwara defines a set $X$ to be $\mathscr{U}$-small if it is isomorphic to a set belonging to $\mathscr{U}$. What does he mean by isomorphism here? He doesn't define it anywhere before. Is it just a bijection?

Answer 1

Yes, it’s just a bijection.${}{}$