Cayley's Theorem (Category Theory)

Theorem
Let $\mathbf C$ be a locally small category.

Then there exists a category $\mathbf D$, subject to:


 * $(1): \quad $ The objects of $\mathbf D$ are sets.
 * $(2): \quad $ The morphisms of $\mathbf D$ are mappings.
 * $(3): \quad \mathbf C \cong \mathbf D$, i.e. $\mathbf C$ and $\mathbf D$ are isomorphic.