Diagram (Category Theory)

Given a category $\mathcal{C}$, a diagram is an index category $\mathcal{I}$ paired with a functor $D:\mathcal{I}\Rightarrow \mathcal{C}$.

Remarks

$D$ is considered finite when its indexing category $\mathcal{I}$ is a finite.
$D$ is considered discrete category
Often $\mathcal{I}$ is a simple category containing just a few objects and morphisms.
For example, a commutative square is a category that contains just 4 objects and 5 non-trivial morphisms (4 sides and 1 diagonal).
This notion is use in the definition of a limit.