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November 11, 2015

Burritos for Category Theorists

Posted by John Baez

You’ve probably heard of Lawvere’s Hegelian taco. Now here is a paper that introduces the burrito to category theorists:

The source of its versatility and popularity is revealed:

To wit, a burrito is just a strong monad in the symmetric monoidal category of food.

Posted at 5:24 PM UTC | Permalink | Followups (25)

November 10, 2015

Weil, Venting

Posted by Tom Leinster

From the introduction to André Weil’s Basic Number Theory:

It will be pointed out to me that many important facts and valuable results about local fields can be proved in a fully algebraic context, without any use being made of local compacity, and can thus be shown to preserve their validity under far more general conditions. May I be allowed to suggest that I am not unaware of this circumstance, nor of the possibility of similarly extending the scope of even such global results as the theorem of Riemann–Roch? We are dealing here with mathematics, not theology. Some mathematicians may think they can gain full insight into God’s own way of viewing their favorite topic; to me, this has always seemed a fruitless and a frivolous approach. My intentions in this book are more modest. I have tried to show that, from the point of view which I have adopted, one could give a coherent treatment, logically and aesthetically satisfying, of the topics I was dealing with. I shall be amply rewarded if I am found to have been even moderately successful in this attempt.

I was young when I discovered by harsh experience that even mathematicians with crashingly comprehensive establishment credentials can be as defensive and prickly as anyone. I was older when (and I only speak of my personal tastes) I got bored of tales of Grothendieck-era mathematical Paris.

Nonetheless, I find the second half of Weil’s paragraph challenging. Is there a tendency, in category theory, to imagine that there’s such a thing as “God’s own way of viewing” a topic? I don’t think that approach is fruitless. Is it frivolous?

Posted at 11:41 PM UTC | Permalink | Followups (14)

November 3, 2015

Cakes, Custard, Categories and Colbert

Posted by John Baez

As you probably know, Eugenia Cheng has written a book called Cakes, Custard and Category Theory: Easy Recipes for Understanding Complex Maths, which has gotten a lot of publicity. In the US it appeared under the title How to Bake Pi: An Edible Exploration of the Mathematics of Mathematics, presumably because Americans are less familiar with category theory and custard (not to mention the peculiar British concept of “pudding”).

Tomorrow, Wednesday November 4th, Eugenia will appear on The Late Show with Stephen Colbert. There will also be another lesser-known guest who looks like this:

Apparently his name is Daniel Craig and he works on logic—he proved something called the Craig interpolation theorem. I hear he and Eugenia will have a duel from thirty paces to settle the question of the correct foundations of mathematics.

Anyway, it should be fun! If you think I’m making this all up, go here. She’s really going to be on that show.

Posted at 10:03 PM UTC | Permalink | Followups (18)