Kerodon

Example 2.4.6.6 (The Homotopy Category of $\operatorname{Top}$). Let $\operatorname{Top}$ denote the category of topological spaces and continuous functions, endowed with the simplicial enrichment $\operatorname{Top}_{\bullet }$ described in Example 2.4.1.5. Then the homotopy category $\mathrm{h} \mathit{\operatorname{Top}}$ is the homotopy category of all topological spaces: the objects of $\mathrm{h} \mathit{\operatorname{Top}}$ are topological spaces, and the morphisms of $\mathrm{h} \mathit{\operatorname{Top}}$ are homotopy classes of continuous maps.