# Kerodon

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

Exercise 7.2.4.2. We say that a partially ordered set $(A, \leq )$ is directed if every finite subset $A_0 \subseteq A$ has an upper bound. Show that $(A, \leq )$ is directed if and only if it is filtered, when regarded as a category.