Kerodon

Example 5.2.0.6. Let $\operatorname{Set}_{\ast }$ denote the category of pointed sets, so that the forgetful functor $\operatorname{Set}_{\ast } \rightarrow \operatorname{Set}$ induces a left covering morphism of simplicial sets $\operatorname{N}_{\bullet }( \operatorname{Set}_{\ast } ) \rightarrow \operatorname{N}_{\bullet }(\operatorname{Set})$ (Example 4.2.3.3). Then the homotopy transport functor $\operatorname{hTr}_{ \operatorname{N}_{\bullet }( \operatorname{Set}_{\ast } ) / \operatorname{N}_{\bullet }(\operatorname{Set}) }$ is isomorphic to the identity functor $\operatorname{id}_{\operatorname{Set}}: \operatorname{Set}\rightarrow \operatorname{Set}$.