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.
Owen Lynch (Apr 26 2022 at 01:46):Is there a logic/internal language take on initial algebras in arbitrary categories? Perhaps toposes? Prerequisite question: is there an "internal" way of defining functors on a topos? I'm well aware of the applications of initial algebras in functional programming, with ana/catamorphisms etc., but in the grand Curry-Howard correspondence, what does that correspond to?
Zanzi (Apr 27 2022 at 15:28):@Owen Lynch you can encode least/greatest fixpoints in a polymorphic lambda calculus, so that corresponds to doing logic in a second-order logic
https://homepages.inf.ed.ac.uk/wadler/papers/free-rectypes/free-rectypes.txt
Mike Shulman (Apr 27 2022 at 15:59):It sounds to me like you're talking about [[W-types]].
Owen Lynch (Apr 28 2022 at 02:54):Yes! OK, that's what I want I think