You're reading the public-facing archive of the Category Theory Zulip server.
To join the server you need an invite. Anybody can get an invite by contacting Matteo Capucci at name dot surname at gmail dot com.
For all things related to this archive refer to the same person.
Morgan Rogers (he/him) (Oct 29 2026 at 12:36):I remember reading an ncatcafe page with a result that a category with certain properties must either be the category of sets and partial functions or a category of vector spaces. Does this ring any bells?
Morgan Rogers (he/him) (Oct 29 2026 at 12:39):I found it
Ivan Di Liberti (Oct 29 2026 at 13:46):Recently Leinster and his master student Maia Woolf worked on this topic, and so did I with my master student Aditya Prakash.
Ivan Di Liberti (Oct 29 2026 at 13:47):https://arxiv.org/abs/2610.31599
Ivan Di Liberti (Oct 29 2026 at 13:47):https://gupea.ub.gu.se/items/40d76650-5854-402c-96f3-a03949dfea3a
Ivan Di Liberti (Oct 29 2026 at 13:49):Centuries ago I gave a talk on this topic too as a form of popularization: https://www.youtube.com/watch?v=9cGgOmnqzvE
Oscar Cunningham (Oct 30 2026 at 15:27):I'm wondering if anyone has looked at the same question over ∞-groupoids. There I think the examples from Set break. Like a circle with a point on it isn't the disjoint union of some space with the point. And a chain complex which has dimension 0 at the bottom can't be the chain complex of any ∞-groupoid. So the analogues of pointed sets and vector spaces aren't always free.
Ivan Di Liberti (Oct 30 2026 at 15:49):Not an answer, but this is related and very interesting: https://arxiv.org/abs/2601.08802. Aditya does a good job in collecting references on the topic in his thesis (including this one).