Since the category $ M $ has only one object, there is only one representable functor on it (up to isomorphism). As an $ M $ - set, the unique representable is the so - called left regular representation of $ M $ , that is, the underlying set of $ M $ acted on by multiplication on the left. Example: Let $ \mathbf{Toph}_* $ be the category whose objects are topological spa\ - ces equipped with a basepoint and whose arrows are homotopy classes of basepoint - preserving continuous maps.