As used in the proof of proposition 3.4.5, the functor ([005B]) is equivalent to the functor \((-)^{\mathrm{fin}}\colon \mathrm{add}\rightarrow\mathrm{st}\) constructed in [ES22, Def. 2.1.17] taking an additive, idempotent-complete \(\infty\)-category \(\mathcal C\) to the stable, idempotent-complete \(\infty\)-category \(\mathcal C^{\mathrm{fin}}\) of finite cell \(\mathcal C\)-modules, explicitly defined to be the smallest full stable subcategory of \(\mathrm{Fun}^{\times}(\mathcal C^\mathrm{op}, \mathrm{Sp})\) (the category of functors taking finite coproducts in \(\mathcal C\) to finite products in \(\mathrm{Sp}\)) containing the image of the Yoneda embedding. The inclusion \(\mathcal C\hookrightarrow \mathcal C^{\mathrm{fin}}\) is induced by the Yoneda embedding.
Original source: arXiv:2401.02956v2
Original source · 2401.02956v2