Warning 2.2.6.4. The notions of isomorphism and strict isomorphism of $2$-categories are somewhat artificial. As in classical category theory, there is notion of equivalence of $2$-categories (Definition 
) which is more general than isomorphism and more appropriate for describing what it means for $2$-categories to be “the same.”
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$