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January 10, 2017

Category Theory in Barcelona

Posted by Tom Leinster

I’m excited to be in Barcelona to help Joachim Kock teach an introductory course on category theory. (That’s a link to — categorical activities in Catalonia have the added charm of a .cat web address.) We have a wide audience of PhD and masters students, specializing in subjects from topology to operator algebras to number theory, and representing three Barcelona universities.

We’re taking it at a brisk pace. First of all we’re working through my textbook, at a rate of one chapter a day, for six days spread over two weeks. Then we’re going to spend a week on more advanced topics. Today Joachim did Chapter 1 (categories, functors and natural transformations), and tomorrow I’ll do Chapter 2 (adjunctions).

I’d like to use this post for two things: to invite questions and participation from the audience, and to collect slogans. Let me explain…

Posted at 6:48 PM UTC | Permalink | Followups (56)

January 4, 2017

Globular for Higher-Dimensional Knottings (Part 3)

Posted by John Baez

guest post by Scott Carter

This is my 3rd post a Jamie Vicary’s program Globular. And here I want to give you an exercise in manipulating a sphere in 4-dimensional space until it is demonstrably unknotted. But first I’ll need to remind you a lot about knotting phenomena. By the way, I lied. In the previous post, I said that the next one would be about braiding. I will write the surface braid post soon, but first I want to give you a fun exercise.

This post, then, will describe a 2-sphere embedded in 4-space, and we’ll learn to try and unknot it.

Posted at 6:08 AM UTC | Permalink | Followups (9)

January 2, 2017

Basic Category Theory Free Online

Posted by Tom Leinster

My textbook Basic Category Theory, published by Cambridge University Press, is now also available free as arXiv:1612.09375.

Cover of Basic Category Theory

As I wrote when I first announced the book:

  • It doesn’t assume much.
  • It sticks to the basics.
  • It’s short.

I can now add a new property:

  • It’s free.

And it’s not only free, it’s freely editable. The book’s released under a Creative Commons licence that allows you to edit and redistribute it, just as long as you state the authorship accurately, don’t use it for commercial purposes, and preserve the licence. Click the link for details.

Posted at 5:43 AM UTC | Permalink | Followups (20)