Coincidences of tensor categories
This week Scott and I were at a wonderful conference on Modular Categories at Indiana University. I find that I generally enjoy conferences on more specific subjects, especially in algebra. Otherwise...
View ArticleSF&PA: Subfactors = finite dimensional simple algebras
Since my next post on Scott’s talk concerns the construction of a new subfactor, I wanted to give another attempt at explaining what a subfactor is. In particular, a subfactor is just a...
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The Witt group, or the cohomology of the periodic table of n-categories
A very popular topic at the Modular Categories conference was the a generalization of the Witt group which is being developed by Davydov, Mueger, Nikshych, and Ostrik. What is this Witt group? Well...
View ArticleWorking equivariantly for the action of a monoidal category
I recently got an email question from Sergey Arkhipov with a question, which I couldn’t answer to my own satisfaction, so I thought I would throw it open to the peanut gallery. One construction I’ve...
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Quaternions and Tensor Categories
As you can tell from the title of this post, I am trying to drag John Baez over to our blog. Let be the ring of quaternions, i.e., with the standard relations. Let -mod be the category of left...
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A hunka hunka burnin’ knot homology
One of the conundra of mathematics in the age of the internet is when to start talking about your results. Do you wait until a convenient chance to talk at a conference? Wait until the paper is ready...
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Concrete Categories
In many introductions to category theory, you first learn the notion of a concrete category: A concrete category is a collection of sets, called the objects of the category and, for each pair of...
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Are Lax Functors Good for Anything?
So I’ve recently been thinking a lot about lax functors between n-categories, trying to get a better feel for what they are and why we should care. I have a few ideas about how certain lax functors...
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Motive-ating the Weil Conjecture Proof
This post concludes a series of posts I’ve been writing on the attempt to prove the Weil Conjectures through the Standard Conjectures. (Parts 1, 2, 3, 4, 5.) In this post, I want to explain the idea of...
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The canonical model structure on Cat
In this post I want to describe the following result, which I think is pretty neat and should be more widely known: Theorem: On the category of (small) categories there is a unique model structure in...
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