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.
Benjamin Merlin Bumpus (he/him) (Jun 22 2023 at 11:35):Hello!
Well Quasi Ordering crops up in many places in mathematics (perhaps most notably in Robertson & Seymour's theorem in graph theory; i.e.what used to be called Wagner's conjecture). WQOs are usually defined as preorders (quasi orders) without infinite antichains; however I was wondering if anyone knows a nice category-theoretic way of defining them? I'd also appreciate any reading suggestions on the topic, if anyone has any :)
John Baez (Jun 22 2023 at 14:27):If anyone knows anything that's not already in [[well-quasi order]], we can add it!
Benjamin Merlin Bumpus (he/him) (Jun 22 2023 at 14:57):Perhaps I should take "page not found" as an encouraging sign that this is worth thinking about :rolling_on_the_floor_laughing:
Morgan Rogers (he/him) (Jun 22 2023 at 15:04):try [[well-quasi-order]] :')
Benjamin Merlin Bumpus (he/him) (Jun 22 2023 at 15:24):ah, thanks! :people_hugging:
John Baez (Jun 22 2023 at 16:19):It's still worth thinking about, since there's not a lot on that page.
Benjamin Merlin Bumpus (he/him) (Jun 22 2023 at 16:35):Agreed; but the coalgebraic formulation seems quite nice!
Todd Trimble (Jul 31 2023 at 17:46):The coalgebraic formulation of [[well-founded relation]] is due to Paul Taylor; he discusses it in his book Practical Foundations of Mathematics. And yes, his notion of well-foundedness is quite far-reaching! It applies to coalgebras of any endofunctor , if has pullbacks and is taut (preserves inverse images of subobjects), and it provides a key for doing recursion theory in a nice categorical way.