Kerodon

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

Example 5.5.3.3. Let $f: X \rightarrow Y$ be a morphism of simplicial sets, which we identify with a functor $\mathscr {F}: [1] \rightarrow \operatorname{Set_{\Delta }}$ (so that $X = \mathscr {F}(0)$ and $Y = \mathscr {F}(1)$). Then the weighted nerve $\int ^{\mathrm{s}}_{[1]}\mathscr {F}$ can be identified with the relative join $X \star _{Y} Y$ of Construction 5.2.4.1.