# Kerodon

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

Corollary 4.3.6.9. Let $q: X \rightarrow S$ be an inner fibration of simplicial sets and let $f: K \rightarrow X$ be any morphism of simplicial sets. Then the restriction map

$X_{/f} \rightarrow X \times _{S} S_{ / (q \circ f)}$

is a right fibration, and the restriction map

$X_{f/} \rightarrow X \times _{ S } S_{(q \circ f)/}$

is a left fibration.

Proof. Apply Proposition 4.3.6.8 in the special case $K_0 = \emptyset$. $\square$