View source for Cone (category theory)

:: '''Note: ''' the definitions for [[Cone (category theory)|cone]] and [[Cocone (category theory)|cocone]] are very similar and contrast each other well, see the page [[cone and cocone compared]] for the definitions compared side by side
__TOC__
==Definition==
Given two [[object (category theory)|objects]] {{M|A}}, {{M|B}} in a [[category]] {{M|\mathscr{C} }}, a ''cone''{{rAITCTHS2010}} is:
* Another object, {{M|X}} from {{M|\mathscr{C} }}, coupled with two [[arrow (category theory)|arrows]] also from {{M|\mathscr{C} }} as follows:
{| class="wikitable" border="1"
|-
| align="center" | {{M|1=\xymatrix{ & A\\ X \ar[ur] \ar[dr] & \\ & B} }}
|-
! Diagram of a cone
|}
This is an instance of a [[wedge (category theory)|wedge]] (a wedge ''to {{M|A}} and {{M|B}}'')
==See also==
* [[Cocone (category theory)|Cocone]] - another kind of [[wedge (category theory)|wedge]] but with arrows from {{M|A}} to {{M|X}} and from {{M|B}} to {{M|X}} rather than outwards from {{M|X}}
* [[Product and coproduct compared]] - parallel definitions of a [[product (category theory)|product]] and [[coproduct (category theory)|coproduct]], which are special wedges
==References==
<references/>
{{Category theory navbox}}
{{Definition|Category Theory}}