Remark 8.3.4.17 (Homotopy Invariance). In the situation of Definition 8.3.4.12, the condition that $\beta $ exhibits $\mathscr {K}$ as corepresented by $G$ depends only on the homotopy class $[\beta ]$ (as a morphism in the homotopy category $\mathrm{h} \mathit{ \operatorname{Fun}( \operatorname{Tw}(\operatorname{\mathcal{D}}), \operatorname{\mathcal{S}})}$) (see Remark 5.6.6.3).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$