dmm: (Default)
I am not sure what (I missed the latest part of the story). But here is a beautiful petition on change.org which says this:

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Waluigi has been scorned by Nintendo yet again, being left out of the roster of Super Smash Bros Ultimate. However, there is still a chance for Waluigi to get his rightly deserved place in the spotlight. Waluigi should appear in the next edition of Higher Algebra.

Indeed, Waluigi fits naturally into the framework of stable ∞-categories, and would probably have been incorporated long ago were Nintendo not so notoriously protective of their copyright. For example, the discussion of the Waldhausen construction in §1.2.2 generalizes without much additional effort to the WAHldhausen construction. It is also worth noting that a careful treatment of the WAHll finiteness obstruction from the ∞-categorical perspective is sorely lacking from the literature.
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(I've read the original Waluigi effect paper. I am going to write more about all this in the comments.)
dmm: (Default)
I used to understand this material in 2012-2014 (I even mentioned it in our own paper published in those years), and it turned out recently that I no longer could reproduce the detailed definitions from memory.

So I am rereading this paper by Isar Stubbe, it's really nice, not excessively difficult (I usually have difficult time reading categorical papers, but this one is a pleasant exception).

Links are in the comments.
dmm: (Default)
When one tries to use category theory for the applied work, a number of questions arise: Is it just too difficult to be used at all by me given my level of technical skills? Is it fruitful enough, and is the fruitfulness/efforts ratio high enough for all this to make sense?

I recently discovered Bruno Gavranović, a graduate student in Glasgow, whose work is promising in this sense. They are really trying hard to keep things simple and also trying to make sure that there are non-trivial applications. Here is one of his essays and papers (March 2021, so it's not the most recent one, but probably the most central):

www.brunogavranovic.com/posts/2021-03-03-Towards-Categorical-Foundations-Of-Neural-Networks.html

(I am posting this here because there are people who read this blog who are interested in applied category theory and like it, not because I am trying to convince those who formed a negative opinion of this subject. I am non-committal myself, I have not decided whether applied categories have strong enough fruitfulness/efforts ratio, but this particular entry seems to be one of the best shots in this sense, so I am going to try to go deeper with their work.)

Update: their collection of papers in the intersection between Category Theory and Machine Learning: github.com/bgavran/Category_Theory_Machine_Learning

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