Suppose \(\mathcal{J}\) is the free category on the graph \(\boxed{1 \rightarrow 2 \leftarrow 3 \rightrightarrows 4 \rightarrow 5}\)
We may draw a diagram \(\mathcal{J}\xrightarrow{D}\mathcal{C}\) inside \(\mathcal{C}\) as below:
\(\boxed{D_1 \rightarrow D_2 \leftarrow D_3 \rightrightarrows D_4 \rightarrow D_5}\)
We can represent this diagram as a cone over the diagram by picking a \(C \in \mathcal{C}\) for which every pair of parallel paths that start from \(C\) are the same.
