Warning 7.7.0.5. Theorem 7.7.0.4 is stronger than its classical counterpart: in the category of sets, small colimits are universal but are generally not strongly universal (see Example 7.7.2.22). In fact, Theorem 7.7.0.4 is in some sense the defining feature of unstable homotopy theory: we will return to this point in Chapter 
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$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$