
Tree Decompositions of Groups: a Letter to Mike Fellows
Hi Mike, You asked: “[w]hat is the analog of treewidth for finite permutation groups? This should have an answer. And the answer should be fairly obvious/deducible (Cf Grothendieck) from the right abstract point of view.“ This blog post is part of my correspondence with Mike Fellows. I’m posting it here for three reasons: (1) I… Read more

CoAdhesive Categories…
Sometimes in math things sound obviously true and that’s exactly how it turns out. Other times, you’re less lucky. Today was one of those days. In this post we’ll see that, although \(\mathsf{Grph}\) is adhesive, \(\mathsf{Grph}^{op}\) isn’t. For a while now, Will Turner and I have been working both with adhesive categories and with \(\mathsf{Grph}^{op}\).… Read more

Tree Decompositions via Lattices
Towards the end of May I visited Johannes Carmesin‘s group at the University of Birmingham. I was there to work with Will Turner on obstructions to compositionality and their categorification. I had an absolute blast. Will and I proved a bunch of new results and this post is about one of them: I’ll tell you… Read more

Diagrammatic Equations
Last fall I read “A diagrammatic view of differential equations in physics” by Evan Patterson, Andrew Baas, Timothy Hosgood and James Fairbanks. They show that you can use diagrams to write down the sorts of equations on manifolds that physicists care about. In this post I’ll try to convey the main ideas of the paper… Read more

Understanding Sheaves §3
In a previous post, we discussed sieves, the sievey definition of Grothendieck topologies and a few exaples thereof. Today we’ll return to sheaves, but this time we do so armed with a better understanding of sites (the “places” in which to define sheaves). This post consists of notes and reflections from reading Daniel Rosiak’s book… Read more

Understanding Sheaves §2
This post is in two parts. The first part consists of notes based on reading Daniel Rosiak’s book Sheaf Theory Through Examples; while the second part of this post (titled “Decompositions as topologies”) consists of new work straight from my notebook. As always the lines are blurred between learning something that is new to me… Read more