Timeline for The urge to combine 1- and 2-morphisms in slicing a 2-category.
Current License: CC BY-SA 2.5
8 events
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| Jun 22, 2022 at 7:16 | history | edited | CommunityBot |
replaced http://front.math.ucdavis.edu/ with https://arxiv.org/abs/
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| Feb 27, 2010 at 23:42 | comment | added | Kevin Walker | Noah: Yes, David's T becomes the shading at the bottom of the rectangle. | |
| Feb 27, 2010 at 23:02 | comment | added | Noah Snyder | Another way to think about the connection between planar algebras and 2-categories is that the planar algebra is a way of studying a 2-category from the point of view of your favorite 1-morphism. This means that certain natural categorical notions translate poorly, but you can talk about say rotation that only make sense once you've chosen a 1-morphism. Since "subfactors" are roughly the same as "Frobenius algebra objects in pivotal categories" you don't lose much by picking that algebra object to always be your favorite object (ie 1-morphism thinking of the monoidal category as a 2-category). | |
| Feb 27, 2010 at 22:42 | comment | added | Noah Snyder | Just to check that I've followed the translation correctly, David's T becomes the shading of the bottom of the rectangle? | |
| Feb 27, 2010 at 15:33 | history | edited | Kevin Walker | CC BY-SA 2.5 |
added 1131 characters in body
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| Feb 27, 2010 at 15:09 | comment | added | Kevin Walker | It's the right paper. I'll expand the original answer to address the rest of your question. | |
| Feb 27, 2010 at 12:15 | comment | added | David Spivak | Hi Kevin, I don't know enough about planar algebras to even understand what I'm seeing here perhaps, but a word search reveals that this paper doesn't mention the word "category" or "morphism." Could it possibly be the wrong paper? If it's the right one, would you point me to the construction? | |
| Feb 27, 2010 at 7:06 | history | answered | Kevin Walker | CC BY-SA 2.5 |