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, ...

This week in our seminar on Cohomology and Computation we continued discussing the bar construction, and drew some pictures of a classic example: Week 26 (May 31) - The bar construction, continued.

When we’ve got a discrete topological group G — or in other words, just a plain old group — we usually call the classifying space of G an Eilenberg–Mac Lane space K (G, 1). This may alternatively be ...

Category Theory and Biology Posted by David Corfield Some of us at the Centre for Reasoning here in Kent are thinking about joining forces with a bioinformatics group. Over the years I’ve caught ...

The data (A, B, α, β) (A,B,\alpha,\beta) is enough to reconstruct our braided 2-group X X up to equivalence. To reconstruct it, we start by taking the category with one object for each element of A A ...

Finally we get to see James Dolan in action, talking about Geometric Representation Theory! While I’ve been focusing on examples, now we’ll start to see the general principles at work in geometric ...

In the penultimate lecture of last fall’s Geometric Representation Theory seminar, James Dolan lays the last pieces of groundwork for the Fundamental Theorem of Hecke Operators. I’ll actually state ...

Those of you who’ve already understood my Abel Symposium talk on Higher gauge theory and elliptic cohomology will find little really new here except a description of characteristic classes for Stringk ...

I certainly have never thought or heard about this idea of yours, Urs, but it sounds believable to me. There are some portions of this idea that are new to me, but make me feel I should have already ...

Let’s take a break from all this type theory and ∞ \infty -stuff and do some good old 2-dimensional category theory. Although as usual, I want to convince you that plain old 2-categories aren’t good ...

The Dynkin diagram of E6 has 2-fold symmetry: So, this Lie group has a nontrivial outer automorphism of order 2. This corresponds to duality in octonionic projective plane geometry! There’s an ...