cones: Details

“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.)”