Free Things Are Complicated (Especially the Sphere Spectrum!)

I’ve spent the last week at CT2025 , which has just come to a close. It was great getting to see so many old friends and meet so many new ones, and every time I go to a CT I’m reminded of just how much category theory there is in the world, as well as just how much I enjoy all of it! Right before this I was in Antwerp for some Noncommutative Geometry , where I learned a ton and met even more new…