Difference between revisions of "Cone (category theory)"
From Maths
(Created page with ":: '''Note: ''' the definitions for cone and cocone are very similar and contrast each other well, see the page cone...") |
m |
||
| Line 14: | Line 14: | ||
* [[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}} | * [[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 | * [[Product and coproduct compared]] - parallel definitions of a [[product (category theory)|product]] and [[coproduct (category theory)|coproduct]], which are special wedges | ||
| + | ** A [[product (category theory)|product]] is a special instance of a cone | ||
==References== | ==References== | ||
<references/> | <references/> | ||
{{Category theory navbox}} | {{Category theory navbox}} | ||
{{Definition|Category Theory}} | {{Definition|Category Theory}} | ||
Latest revision as of 22:27, 28 February 2016
- 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
[hide]Definition
Given two objects A, B in a category C, a cone[1] is:
- Another object, X from C, coupled with two arrows also from C as follows:
| Diagram of a cone |
|---|
This is an instance of a wedge (a wedge to A and B)
See also
- Cocone - another kind of wedge but with arrows from A to X and from B to X rather than outwards from X
- Product and coproduct compared - parallel definitions of a product and coproduct, which are special wedges
- A product is a special instance of a cone
References
| ||||||||||||||||||||||||||||||||
