Talk:Duality (mathematics)
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[edit] Explanation of edit
So I put in this explanation -- "Usually duality is associated with some sort of general operation, where finding the "dual" of an object twice retrieves the original object (hence the "duality"). This does not preclude the possibilty that an object is its own dual, but there should be at least some objects which are distinct from their duals."
I'm not sure this is the best wording, but I think it conveys the "feeling" behind duality which transcends the categories in place.
Demorgan's dual: objects - binary operators, operation - swapping and and or and negating. Dual polyhedron: objects - polyhedra, operation: faces to vertices Dual spaces: objects - vector spaces, operation: taking linear functionals
[edit] older stuff
Further dualities include;
- Alexander duality
- Cartier duality
- dual problem in optimization theory
- duality of abelian varieties
- Kolmogorov duality
- Lefschetz duality
- S-duality (homotopy theory)
- Steenrod duality
- Tate-Poitou duality
Charles Matthews 09:43, 21 Apr 2004 (UTC)
Actually I take the dual in dual numbers to imply double, rather than any duality.
Charles Matthews 07:03, 28 Apr 2004 (UTC)
What does the phrase "is dual to" mean? helohe 21:05, 7 Jun 2005 (UTC)
[edit] category theory
Shouldn't there be a reference to the notion of 'dual' from category theory? If someone with more expertise does not add it in the next days, I will give it a go. Ringan 22:50, 16 October 2005 (UTC)Erik Douglas
[edit] "Geometric" duality?
The planar graph example in the "geometric" section isn't particularly geometric: it's topological. I nuked the word 'geometric' from the link for that reason, but now it doesn't fit in its section. Bhudson 22:45, 8 December 2006 (UTC)
