Terminology for natural transformations can also be applied to cocones. For example, a component of a cocone is a component of the natural transformation ; that is, the component for each object of is the morphism .
A morphism of cocones is a morphism in such that for all objects in (symbolically ); the composition being the composition of underlying morphisms in . Thus cocones form a category whose initial object if it exists is a colimit of .
Revised on March 28, 2012 07:29:04
by Urs Schreiber