CatGloss

Since the category M M has only one object, there is only one representable functor on it (up to isomorphism). As an M M - set, the unique representable is the so - called left regular representation of M M , that is, the underlying set of M M acted on by multiplication on the left. Example: Let Toph \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.