Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Remark 3.1.3.11. Suppose we are given a commutative diagram of simplicial sets

\[ \xymatrix { A \ar [r]^{f} \ar [d]^{i} & X \ar [d]^{q} \\ B \ar [r]^{g} \ar@ {-->}[ur]^{ \overline{f} } & S. } \]

Then the simplicial set $\operatorname{Fun}_{A/ \, /S}( B, X)$ can be identified with the fiber of the induced map

\[ \operatorname{Fun}(B,X) \rightarrow \operatorname{Fun}(A,X) \times _{ \operatorname{Fun}(A,S) } \operatorname{Fun}(B,X) \]

over the vertex given by the pair $(f,g)$.