Bousfield-Kan completion as a codensity $\infty$-monad

Emmanuel Dror Farjoun, Sergei O. Ivanov

Working in the setting of $\infty$-categories, we develop a general theory of the codensity monad $T_{\mathcal{D}}$ associated with a full subcategory $\mathcal{D}\subseteq \mathcal{…