cocone

A cocone under a diagram is an object equipped with morphisms from each vertex of the diagram into it, such that all new diagrams arising this way commute. A cocone which is universal is a colimit. The dual notion is cone . Let and be categories; we generally assume that is small. Let be a functor (called a diagram in this situation). Then a cocone (or inductive cone) over is a pair of an object and a natural transformation (where is the constant diagram , , ). In other words, a diagram as...