Cocone (category theory)
From Maths
 Note: the definitions for cone and cocone are very similar and contrast each other well, see the page cone and cocone compared for the definitions compared side by side
Contents
Definition
Given two objects [ilmath]A[/ilmath], [ilmath]B[/ilmath] in a category [ilmath]\mathscr{C} [/ilmath], a cocone^{[1]} is:
 Another object, [ilmath]X[/ilmath] from [ilmath]\mathscr{C} [/ilmath], coupled with two arrows also from [ilmath]\mathscr{C} [/ilmath] as follows:
[ilmath]\xymatrix{ A \ar[dr] & \\ X & \\ B \ar[ur] &}[/ilmath] 
Diagram of a cocone 

This is an instance of a wedge (a wedge from [ilmath]A[/ilmath] and [ilmath]B[/ilmath])
See also
 Cone  another kind of wedge but with arrows outwards from [ilmath]X[/ilmath] instead
 Product and coproduct compared  parallel definitions of a product and coproduct, which are special wedges
 Coproduct  a special instance of a cocone
References
