Remark 4.3.5.4. Construction 4.3.5.1 and Variant 4.3.5.3 are opposite to one another. More precisely, if $f: K \rightarrow X$ is a morphism of simplicial sets and $f^{\operatorname{op}}: K^{\operatorname{op}} \rightarrow X^{\operatorname{op}}$ denotes the induced map of opposite simplicial sets, then we have a canonical isomorphism of simplicial sets $(X_{/f})^{\operatorname{op}} \simeq (X^{\operatorname{op}})_{f^{\operatorname{op}}/ }$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$