Cone

Summary

A cone over a diagram $D \colon J \to \mathcal{C}$ is an object $N$, the apex, with a morphism from $N$ to each object $D(j)$ of the diagram. All triangles formed with the morphisms of the diagram must commute. Dually, a cocone has morphisms from the objects of the diagram into a common object. Limits are the universal cones and colimits are the universal cocones.