A cone is an object (the apex) and a natural transformation from a constant functor (whose image is the apex of the cone and its identity morphism) to a diagram functor. Its components are projections from the apex to the objects of the diagram and it has a “naturality triangle” for each morphism in the diagram. (A “naturality triangle” is just a naturality square which is degenerate at its apex side.)

My father did not magnanimously toss fish to the admiring multitudes, and most likely he did not beckon to the catfish, which then leapt suicidally into our boat.

He handcarried it all the way. sir. It took him 30 days.

The neurologist pointed to a troubling trough in the pattern of his brain-waves.