Merlin's Notebook

My good friend Zoltan Kocsis and I finally got our paper “Degree of Satisfiability in Heyting Algebras” published in the Journal of Symbolic Logic. Yay! Since Zoltan is half-way across the world, we can’t grab a beer together and celebrate, so instead here’s a celebratory blog post (you can find the ArXiv version of our… Read more

Recently I have been thinking a lot about pullbacks of graphs and it really is frustrating at times because they’re much harder to think about compared to colimits. It turns out that there is an obvious (in hindsight) reason for this and I thought it would be nice to tell you about it. While thinking… Read more

During Thanksgiving week I went to Wytham Abbey, a manor house in Oxfordshire where the “Workhop on Non-Compositionality in Complex Systems” was taking place. The workshop (organized by Matteo Cappucci and Jules Hedges) was centered around four papers that covered the theme of compositional patterns and emergence therein. I wrote one of them (the one… Read more

Hi Mike, You asked: “[w]hat is the analog of tree-width 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

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

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