The free group $F(S)$ is the group given by a set $S$ with the universal property: For every group $G$ and map $f: S \to G$ there is a unique homomorphism $\phi: F(S) \to G$, such that $\phi \circ i = f$ where $i: S \to F(S)$ is the inclusion.
If we ignore that $S$ is a set and $F(S)$ and $G$ are groups, $F(S)$ could be the colimit of the diagram with exactly one object.
Is this true? Is the universal property generally a colimit of a diagram with one object? And if it's true how can one precise this given that $S, F(S)$ and $G$ are not in the same category?