# Kerodon

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Example 5.2.8.3. Let $\operatorname{Set}_{\ast }$ denote the category of pointed sets (Example 4.2.3.3), and let $V: \operatorname{Set}_{\ast } \rightarrow \operatorname{Set}$ denote the forgetful functor $(X,x) \mapsto X$. Then the induced map $\operatorname{N}_{\bullet }(V): \operatorname{N}_{\bullet }( \operatorname{Set}_{\ast } ) \rightarrow \operatorname{N}_{\bullet }(\operatorname{Set})$ is a cocartesian fibration (in fact, it is a left covering map), whose fiber over an object $X \in \operatorname{N}_{\bullet }(\operatorname{Set})$ can be identified with the set $X$. For every pair of sets $X$ and $Y$, the evaluation map

$\operatorname{ev}: \operatorname{Hom}_{\operatorname{Set}}(X,Y) \times X \rightarrow Y \quad \quad (f,x) \mapsto f(x)$

is given by parametrized covariant transport (in the sense of Definition 5.2.8.1).