Remark 7.1.2.3. In the situation of Definition 7.1.2.1, the condition that $e: K \rightarrow \operatorname{Hom}_{\operatorname{\mathcal{C}}}(X,Y)$ exhibits $X$ as a power of $Y$ by $K$ (or $Y$ as a copower of $X$ by $K$) depends only on the homotopy class $[e] \in \pi _0( \operatorname{Fun}(K, \underline{\operatorname{Hom}}_{\operatorname{\mathcal{C}}}(X,Y) ) )$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$