# Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$

Corollary 7.3.6.3. Let $\operatorname{\mathcal{C}}$ and $\operatorname{\mathcal{D}}$ be $\infty$-categories, and let $\delta : K \rightarrow \operatorname{\mathcal{C}}$ be a diagram. Suppose that every diagram $F_0: K \rightarrow \operatorname{\mathcal{D}}$ has a left Kan extension along $\delta$. Then the restriction functor

$\operatorname{Fun}( \operatorname{\mathcal{C}}, \operatorname{\mathcal{D}}) \xrightarrow { \circ \delta } \operatorname{Fun}(K, \operatorname{\mathcal{D}})$

has a left adjoint, which carries each diagram $F_0: K \rightarrow \operatorname{\mathcal{D}}$ to a left Kan extension of $F_0$ along $\delta$.