Cats and Types, Side by Side (qtcat2026)

As a type theorist who hangs out with category theorists, I am always fascinated by what we share and by how we differ. What do some of us fuss over that others just take for granted? I gave a talk at Topos Institute with some observations in this area five years ago. In this talk, I'll look at what has changed, including me, in those five years. In particular, I have experienced the need to have more to say about monoidal structure - juxtaposition - as well as composition. I'll talk about opportunities and obstacles for using appropriate types to work with these cats. Licensed to the public under https://creativecommons.org/licenses/by/4.0/ about this event: https://pretalx.c3voc.de/qtcat-2026/talk/WDTZ3Q/