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Example (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 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.