# Cone (category theory)

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

## Definition

Given two objects [ilmath]A[/ilmath], [ilmath]B[/ilmath] in a category [ilmath]\mathscr{C} [/ilmath], a cone[1] is:

• Another object, [ilmath]X[/ilmath] from [ilmath]\mathscr{C} [/ilmath], coupled with two arrows also from [ilmath]\mathscr{C} [/ilmath] as follows:
 Diagram of a cone [ilmath]\xymatrix{ & A\\ X \ar[ur] \ar[dr] & \\ & B}[/ilmath]

This is an instance of a wedge (a wedge to [ilmath]A[/ilmath] and [ilmath]B[/ilmath])