Wedge (category theory)

Note: the page Cone and cocone compared redirects here as this is basically a discussion page on how the two differ (which exists because of the page Products and coproducts compared)

Definition

For a pair of objects $A$ and $B$ in a category $\mathscr{C}$ we define:

Wedge to the pair $A$, $B$	Wedge from the pair $A$, $B$
is an object $X$ in $\mathscr{C}$ together with a pair of arrows (also from $\mathscr{C}$) as follows:
$\xymatrix{ & A \\ X \ar[ur] \ar[dr] & \\ & B}$	$\xymatrix{A \ar[dr] & \\ & X \\ B \ar[ur] & }$
(AKA: cone)	(AKA: cocone)