Wedge (category theory)
From Maths
- 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 Product and coproduct compared)
Contents
Definition
For a pair of objects [ilmath]A[/ilmath] and [ilmath]B[/ilmath] in a category [ilmath]\mathscr{C} [/ilmath] we define[1]:
| Wedge to the pair [ilmath]A[/ilmath], [ilmath]B[/ilmath] | Wedge from the pair [ilmath]A[/ilmath], [ilmath]B[/ilmath] |
|---|---|
| is an object [ilmath]X[/ilmath] in [ilmath]\mathscr{C} [/ilmath] together with a pair of arrows (also from [ilmath]\mathscr{C} [/ilmath]) as follows: | |
| [ilmath]\xymatrix{ & A \\ X \ar[ur] \ar[dr] & \\ & B}[/ilmath] | [ilmath]\xymatrix{A \ar[dr] & \\ & X \\ B \ar[ur] & }[/ilmath] |
| (AKA: cone) | (AKA: cocone) |
References
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