Diagram

A diagram \(\mathcal{D}\) in a category \(\mathcal{C}\)

• A functor \(\mathcal{J}\xrightarrow{D}\mathcal{C}\) from any category \(\mathcal{J}\) called the indexing category of the diagram \(D\).

• We say \(D\) commutes if \(D(f)=D(f')\) for every parallel pair of morphisms \(f,f'\) in \(\mathcal{J}\)