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Peiyuan Zhu (Nov 04 2022 at 23:45):Does anyone here has good reference to Catastrophe theory and its computation methods?
Peiyuan Zhu (Nov 04 2022 at 23:46):My main question concerns what does it has to do with analogy making
Peiyuan Zhu (Nov 05 2022 at 00:31):It seems like it has something to do with cobordism
Simon Burton (Nov 05 2022 at 13:48):Have you read much about Morse theory?
Morgan Rogers (he/him) (Nov 06 2022 at 12:57):@Peiyuan Zhu please stop posting in Beginner questions; the questions you ask are not beginner questions in category theory, which is what that topic is for.
Morgan Rogers (he/him) (Nov 06 2022 at 13:03):Peiyuan Zhu said:
This passage is extremely speculative. There is scope to make the connection he's pointing to precise, but there is not enough content in that passage to reconstruct useful insights, in my opinion. I'm not surprised you have a lot of questions about it.
Morgan Rogers (he/him) (Nov 06 2022 at 13:04):Peiyuan Zhu said:
"What homotopy type theory
does is take observations such as these not merely as an analogy, but as the first steps of a
series of levels."How to understand this?
As a metaphor. It doesn't have enough precision to do more for your understanding than being evocative.
Morgan Rogers (he/him) (Nov 06 2022 at 13:10):Peiyuan Zhu said:
What does the "cohesion" mentioned here has to do with cohesive topos?
Cohesive toposes are supposed to be categories whose objects behave like spaces in terms of the relationship between their points and their "parts". The word "cohesion" is being used in the same sense in both cases, but there is otherwise no specific relationship between these concepts (at least not one which has been explored in any depth, to my knowledge).
Morgan Rogers (he/him) (Nov 06 2022 at 13:13):Peiyuan Zhu said:
But how to make sense of that recursive definition?
To use more conventional terminology, the powerset of order 1 of a set is the usual powerset , the powerset of order 2 is and so on.
Notification Bot (Nov 06 2022 at 16:42):9 messages were moved here from #learning: questions > HoTT and philosophy by Matteo Capucci (he/him).
Peiyuan Zhu (Nov 06 2022 at 19:59):Morgan Rogers (he/him) said:
Peiyuan Zhu please stop posting in Beginner questions; the questions you ask are not beginner questions in category theory, which is what that topic is for.
Do I need a moderator to create new topics?
Peiyuan Zhu (Nov 06 2022 at 20:01):Morgan Rogers (he/him) said:
Peiyuan Zhu said:
But how to make sense of that recursive definition?
To use more conventional terminology, the powerset of order 1 of a set is the usual powerset , the powerset of order 2 is and so on.
So for , , ? Seem to be a computationally intractable construction he's proposing? Is that the same as the non-well-founded set of Peter Azcel, hypersets of Jon Barwise and John Perry?
Jean-Baptiste Vienney (Nov 06 2022 at 20:02):Peiyuan Zhu said:
Morgan Rogers (he/him) said:
Peiyuan Zhu please stop posting in Beginner questions; the questions you ask are not beginner questions in category theory, which is what that topic is for.
Do I need a moderator to create new topics?
Click on the three points on the right of the stream and then "New topic"
Peiyuan Zhu (Nov 06 2022 at 20:03):Jean-Baptiste Vienney said:
Peiyuan Zhu said:
Morgan Rogers (he/him) said:
Peiyuan Zhu please stop posting in Beginner questions; the questions you ask are not beginner questions in category theory, which is what that topic is for.
Do I need a moderator to create new topics?
No, and that's super easy: for a new stream click on the + on the right of "STREAMS" and then on "Create a stream". But I guess you mean a topic. For this click on the three points on the right on the stream and then "New topic"
Are people only notified by existing streams? If I open a new stream will other people be able to see it?
Jean-Baptiste Vienney (Nov 06 2022 at 20:05):I think they will see it if you create a new stream but will be notified of the messages only if they subscribe to the stream. For a new topic, they will be notified if they are subscribed to the stream.
Morgan Rogers (he/him) (Nov 06 2022 at 22:04):Indeed, while it's possible to create new streams, please do not unless your topic does not fit into an existing stream.
John Baez (Nov 06 2022 at 23:05):Yes - new topics are easy to create and you shouldn't be shy of doing so, but you should avoid creating new streams unless it's absolutely necessary.
Basically, you should only create a new stream if people will want to create many topics in this new stream! And new streams should have carefully chosen general names.
Peiyuan Zhu (Nov 29 2022 at 00:41):Simon Burton said:
Have you read much about Morse theory?
I didn't. Is there a good entry book for this topic?
Peiyuan Zhu (Nov 29 2022 at 04:43):Can anyone help with moving this entire discussion to "dynamical systems" under #learning: questions?
Simon Burton (Dec 01 2022 at 14:25):The wikipedia page on Morse theory seems reasonable.. Anyway, this is one way to decompose cobordisms into primitive catastrophes, or singular events, which are the critical points. Example: a pair-of-pants has one critical point, which is a saddle, where two circles meet to become one circle. Then there's an algebraic interpretation of these events, which is what the cobordism hypothesis is about. You might enjoy the book by Joachim Kock "Frobenius algebras and 2D topological quantum field theories".
