Cocone (category theory)

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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


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


  1. An Introduction to Category Theory - Harold Simmons - 1st September 2010 edition