Before I start talking about what I want, I should point out that pointed category is pretty much the lowest generalization of abelian category, which is an important concept when thinking about algebra from a categorical perspective. What is a pointed category? What should the term 'pointed category' refer to? Let's start with a simpler case. … Continue reading Pointed category: why is it defined that way?
A common mistake people make is to think that a continuous bijection is a homeomorphism. This is a reasonable mistake. A bijection is an isomorphism of sets. A bijective homomorphism of groups is an isomorphism of groups. In most algebraic settings I can think of this pattern holds. But it is not true of topological … Continue reading Homeomorphism is not just continuous bijection
I don't often think about combinatorics, but when I was on a plane recently (coming back from the Netherlands), I started thinking about a question I've just kept in the back of my mind for a few years. You can read about the simplex category here. In this blog post I'll go through the exact … Continue reading Counting the simplex category
For the past two weeks, I've been in the Netherlands for the Applied Category Theory workshop and conference. I stayed in a suburb called Katwijk aan Zee. I ended up working with Pawel Sobocinksi's group on modelling of open and interconnected systems. I only went to Leiden, so all the pictures are from there. In … Continue reading Applied Category Theory in the Netherlands, photo dump