Exercise 5. If you know about coproducts, you can show that F + G is the coproduct of F and G in the category of species, Set E, which we defined last time. Exercise 6. If you know about products, you ...

Following SoTFom II, which managed to feature three talks on Homotopy Type Theory, there is now a call for papers announced for SoTFoM III and The Hyperuniverse Programme, to be held in Vienna, ...

The history This paper got its start in April 2007 when Allen Knutson raised a question about Schur functors here on the n n -Category Café. I conjectured an answer, and later Todd Trimble refined the ...

It’s now easy to get inverses: whenever you have a monoid where every element g has both a left inverse (here 1 / g) and a right inverse (here g \ 1), they must be equal, so we can take either one to ...

Did you ever have a math teacher who seemed grumpy? At least in America, schools are full of them. Why do they get that way? Maybe it’s because they spent too long controlling rowdy students, or ...

More sophisticated sheaf models would repair such defects by considering not all presheaves on S, but sheaves with respect to a Grothendieck topology on S which takes into account such coverings. The ...

Namely if there is, for instance, a whole line of critical points, we say that all points on this line are isomorphic configurations. What we are interested in, then, are the isomorphism classes of ...

You might think this doesn’t say anything about the familiar concerns of linear algebra - but wait a moment. Fix an endomorphism T T of V V, a finite-dimensional complex vector space. For λ ∈ C ...

It takes its minimum value, 0, when the distribution is concentrated at one point (that is, some pi is 1), and its maximum value, σα(1 / n), when the distribution is uniform (p1 = ⋯ = pn = 1 / n). The ...

Here’s the summary from the BBC website: In this one-off documentary, David Malone looks at four brilliant mathematicians - Georg Cantor, Ludwig Boltzmann, Kurt Gödel and Alan Turing - whose genius ...

With your help, I would like to start amassing a collection of wisdom on gnarly issues in physics. Let’s start with dimensional analysis. I thought I had this pretty much figured out, until Kehrli ...

Grothendieck’s Galois theory In 1960 and 1961 Grothendieck developed a new approach to Galois theory in a series of seminars that got written up as SGA1. This is sometimes called Grothendieck’s Galois ...