Cocone (Category Theory)

In category theory, a cocone for a diagram $D:\mathcal{I}\Rightarrow \mathcal{C}$ is a $\mathcal{C}$ object, $d$ paired with a Natural Transformation $N:D\Rightarrow \Delta d$ where $\Delta d:\mathcal{I}\Rightarrow \mathcal{C}$ is the constant functor. Naturality tells us that for all $f:a\to b$ in $D$, the cocone commutes with $f$.