Andrew Stacey

Andrew Stacey
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By: Andrew Stacey
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Andrew Stacey

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Fri, 12th Feb 2010 (Seminars)

Category Theory: Making Mathematical Pearls Since the 1940s

How to make a pearl:

  1. Find something irritating.
  2. Cover it in something most think vaguely disgusting.
  3. Leave it to one side until someone comes along and says "That's beautiful".

If you are an oyster, this involves grit and mucus (generally agreed upon as being a bit disgusting by all except small children) and the result is a pearl. For a mathematician, irritating things include: being told something can't be done, being told that two things are similar but for there to be no connection between the two, and being told that something is true but with no reason behind it. Category theory grew out of getting rid of these irritations by covering them with structures and axioms (which most find faintly displeasing but a few find fascinating). But, over time, it has produced its fair share of gems.

categorical pearls

This talk is a beamer presentation and uses TikZ for the drawings. I now use lots of my own macros for beamer presentations so it's not practical to make the source available.

Please do not print out the beamer or trans versions of this talk. They are intended solely for on-screen viewing (the trans version has just one overlay per frame so is a little simpler to step through). If you really want to print something out (why?) then print out the handout version.

  • Presentation version in PDF. This is what is actually shown on the screen.
  • Slides version in PDF. For the most part, this is a one slide per frame version of the presentation.
  • Handout version in PDF. Note: this uses pgfpages to format it as 4-up. With double-sided printing, this only uses 4 pieces of paper. Neat, huh?
  • Extras:
    • There weren't any fundamentally new pictures in this presentation. The torus picture can be found in my talks on Smootheology.
    • The "Eckmann-Hilton" dance was made using processing. In the seminar, it was set to Danse des Mirlitons from the Nutcracker Suite by Tchaikovsky. Also, in the seminar it was mildly interactive. However, as an interactive program it is a little big for an applet and the interactivity was very limited anyway so I'm only making it available as a movie, mpg (2Mb) or avi (8Mb), and as source code.

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Last modified on:
Fri, 5th Nov 2010