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 which the weak equivalences are the equivalences of categories.

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Conference on Higher Gauge Theory, Quantum Gravity, and Topological Field Theory

In February there is going to be a workshop and school dedicated to exploring the interactions of Quantum Gravity, Higher Gauge Theory, and Topological Field Theory. I’m excited about the chance to share ideas and hopefully create some new mathematics.

The conference will take place in Lisbon, Portugal, and yours truly will be giving one of the mini-courses for the school (the topic is going to be the classification of extended 2D tqfts, something near and dear to my heart). Of course that makes me really excited, but I am also excited about the other topics too and I think the mix of ideas will be invigorating. For more info look below the break.

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Chromatic Homotopy II or how I learned to stop worrying and love LaTeXing in Real Time

I am currently taking course notes for Jacob Lurie’s class on Chromatic Stable Homotopy in real time in Latex. This is not the first time I have taken course notes live and in tex, and when people see it happening they often ask me about it.

I wanted to write an update about Jacob Lurie’s class on Chromatic Stable Homotopy and mention some of exciting and beautiful things happening in that course, but as I started writing this post I found that it was morphing into a sort advice post on how to LaTeX in real time. Since there is obvious appeal, I’ve decided to run with it and collect all the advice, tips, and tricks on how to LaTeX in real time that I’ve gathered from the wild.

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Chromatic Stable Homotopy Theory and the AHSS

Now that we’ve all gotten over the excitement surrounding the new iPad, I wanted to talk about something else which I actually find very exciting (unlike the iPad). This semester Jacob Lurie is giving a course on Chromatic Homotopy Theory. This is a beautiful picture which relates algebraic topology and algebraic geometry. Hopefully with Jacob at the helm we’ll also see the derived/higher categorical perspective creeping in. This seems like a great opportunity the learn this material “in my heart”, as my old undergraduate advisor used to say.

And with most of our principal bloggers distracted by MathOverflow, it also seems like a good time to experiment with new media. So here’s the plan so far:

  • During lectures I’m going to be live-TeXing notes, which I’ll flush out and post to my website. (Jacob’s also posting his own notes!)
  • In addition, I’ll try to post blog articles (like this one) about related topics or topics I find interesting/confusing.
  • There might be a little MO action thrown in for fun.
  • The offshoot is that today I want to talk a little about chromatic homotopy and about the Atiyah-Hirzebruch Spectral Sequence.

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    Lurie on TFTs

    This morning Jacob Lurie posted a draft of an expository paper on his work (with Mike Hopkins) classifying extended (infinity, n)-categorical topological field theories and their relation to the Baez-Dolan cobordism hypothesis.

    Should make for some intersting bedtime reading…