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.
Chris Grossack (they/them) (Sep 27 2024 at 01:27):Earlier on mathstodon @Martín Hötzel Escardó mentioned he would consider swinging by the zulip and talking about constructive math, but he wanted to know that there were ongoing conversations that would interest him. So I'm posting this thread to lure him in (though I'm also happy to hear what other people think of the topic).
Chris Grossack (they/them) (Sep 27 2024 at 01:28):I know that domain theory is useful for the semantics of programming languages, and I think this has to do with an object with , which makes fixed point combinators and general recursion possible... But this is about all I know. I don't really know what domains are, why they're still useful/interesting nowadays, how they relate to constructive topology, etc.
I mean, I kind of know a few things about some of these things, but I would love to hear other people who know more say more interesting things about them!
Madeleine Birchfield (Sep 27 2024 at 01:31):Chris Grossack (they/them) said:
Earlier on mathstodon Martín Hötzel Escardó mentioned he would consider swinging by the zulip and talking about constructive math, but he wanted to know that there were ongoing conversations that would interest him.
Is he interested in real analysis and constructive topology? I have a few questions on those topics.
Chris Grossack (they/them) (Sep 27 2024 at 01:32):He's certainly interested in constructive topology. I'm not sure about analysis. We'll see what he says if he decides to swing by ^_^
Ryan Wisnesky (Sep 27 2024 at 01:43):In addition to having D ~ D^D, you get that the computable functions are exactly the continuous ones, letting you use topology to study things like non-termination vs termination
Chris Grossack (they/them) (Sep 27 2024 at 01:57):Oh, cool! Is that a theorem, or baked into the definition?
John Baez (Sep 27 2024 at 15:42):Martin, who is too busy to write here but somehow not too busy to read this stuff and reply on Mathstodon, denies what Ryan said.
Ryan Wisnesky (Sep 27 2024 at 18:14):to be sure, the correct statement (taken from Martin) is: "Every computable function is continuous, but the converse fails in general." my point is more, this correspondence and its technical specifics are one reason why domain theory is useful