Kerodon

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

Corollary 3.5.2.14. Let $m$ and $n$ be integers, let $X$ be a Kan complex which is $(m+n)$-connective, and let $B$ be a simplicial set of dimension $\leq m$. Then the Kan complex $\operatorname{Fun}(B,X)$ is $n$-connective.

Proof. Apply Corollary 3.5.2.12 in the special case $A = \emptyset $ (or Corollary 3.5.2.13 in the special case $Y = \Delta ^0$). $\square$