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1. Page created, but author did not leave any comments.

Egbert Rijke

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeAug 2nd 2020
• (edited Aug 2nd 2020)

Thanks to Egbert for starting this! (We had been discussing behind the scenes).

I have now added redirects and changed capitalization in order to make the last three hyperlinks come out properly:

The second and third of these would deserve page of their own. If so, just remove the redirect and create the dedicated page.

• CommentRowNumber3.
• CommentAuthorEgbertRijke
• CommentTimeAug 2nd 2020

The spam detector of the nlab prevents me from making further edits. What can I do about this?

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeAug 2nd 2020

Try to add smaller pieces at a time. If all fails, post the code to the nForum here and I can insert it.

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeAug 2nd 2020
• (edited Aug 2nd 2020)

I have added the pointer to the GitHub page! :-)

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeAug 2nd 2020
• (edited Aug 2nd 2020)

added hyperlinking to a few more of the technical terms (such as type theory, homotopy theory and Agda)

• CommentRowNumber7.
• CommentAuthorEgbertRijke
• CommentTimeAug 2nd 2020

Thanks so much!

And I figured it out with the smaller edits :)

• CommentRowNumber8.
• CommentAuthorEgbertRijke
• CommentTimeAug 2nd 2020

I tried to include the links in a way that doesn’t suggest that the pdf is what the book actually will look like (because these course notes are quite old).

• CommentRowNumber9.
• CommentAuthorDavidRoberts
• CommentTimeAug 2nd 2020

Listed page lengths for the two versions of the course notes. Makes it clear that the later notes are shorter, not longer!

2. I included the section titles to give an idea of the outline of the book.

Egbert Rijke

• CommentRowNumber11.
• CommentAuthorUrs
• CommentTimeAug 4th 2020
• (edited Aug 4th 2020)

Might you (or anyone reading here) have 5 minutes to give “Univalent Foundations for Mathematics” a little entry of its own, with a sentence on the basic idea? (So that it does not just redirect to the HoTT book.)

And while we are at it, let’s rename to “Rezk-Lurie-Voevodksy’s univalent foundations” – because, apart from the inventive terminology, the observation of univalent universes first appears in Jacob’s HTT 6.1.6 (published 2009), where it is attributed to private conversation with Charles. Voevodsky’s first note on it seems to be from 2010.

• CommentRowNumber12.
• CommentAuthorGuest
• CommentTimeAug 4th 2020
Ok, I will do it
• CommentRowNumber13.
• CommentAuthorEgbertRijke
• CommentTimeAug 4th 2020
That last comment was by me. Sorry, I did not realise that I wasn't logged in
• CommentRowNumber14.
• CommentAuthorAli Caglayan
• CommentTimeAug 4th 2020
@Urs It doesn't seem correct to me to rename it "Rezk-Lurie-Voevodsky's univalent foundations". I think you are conflating two separate issues here. The observation that higher toposes have univalent universes is not the same as a "univalent foundation". The latter is AFAIK something that Voevodsky started for foundational reasons, whilst the former is typically attributed to Voevodsky in the form of the univalence axiom. I think the former can be renamed "Rezk-Lurie-Voevodsky univalence" if you really want, but my point is that it has little to do with the idea of "univalent foundations".
• CommentRowNumber15.
• CommentAuthorEgbertRijke
• CommentTimeAug 4th 2020
Let's have that discussion at the page about the univalent foundations for mathematics
• CommentRowNumber16.
• CommentAuthorUrs
• CommentTimeAug 4th 2020

The latter is AFAIK something that Voevodsky started for foundational reasons, whilst the former is typically attributed to Voevodsky

That’s a telling slip of tongue there ;-)

• CommentRowNumber17.
• CommentAuthorGuest
• CommentTimeJan 14th 2022
This page needs an update. It is 2022 already and the textbook has not been published yet.
• CommentRowNumber18.
• CommentAuthorGuest
• CommentTimeJan 18th 2022

To the guest at 17: the textbook isn’t published yet, but Egbert Rijke did release another preprint here.

• CommentRowNumber19.
• CommentAuthorUrs
• CommentTimeJan 19th 2022

Not sure where this link was intended to point, but the entry Introduction to Homotopy Type Theory (which #17 is referring to) lists several links to preprint versions.

• CommentRowNumber20.
• CommentAuthorGuest
• CommentTimeJan 19th 2022

Urs, this preprint was only released on September 2021 as said in the pdf file itself, so isn’t actually linked in the article.

• CommentRowNumber21.
• CommentAuthorGuest
• CommentTimeJan 19th 2022
It also has 36 chapters instead of 15 so the table of contents needs to be modified as well.
• CommentRowNumber22.
• CommentAuthorUrs
• CommentTimeJan 19th 2022

I still don’t know which preprint you mean, as the link in your #18 is broken! (Maybe I should have said this more explicitly in #19. Please check the link and let us know where you are pointing us to.)

• CommentRowNumber23.
• CommentAuthorDavidRoberts
• CommentTimeJan 19th 2022

It’s a link to a pdf on the HoTT Zulip, this is the thread where it is.

• CommentRowNumber24.
• CommentAuthorUrs
• CommentTimeJun 16th 2022

I have deleted the obsolete line

…and is expected to be published in 2021.

If anyone knows more, please drop a note.

3. A new draft of this textbook has been put out to the public in the HoTTEST Summer School 2022’s github repo

There are some changes from the chapter listing on this article.

• CommentRowNumber26.
• CommentAuthorUrs
• CommentTimeJul 5th 2022

Thanks. I have added the pointer to the entry (here)

4. The changes in the section titles are as follows:

• Section 7 of chapter 1 is renamed to “Modular arithmetic via the Curry-Howard interpretation”
• A new section 8 named “Decidability in elementary number theory” is added at the end of chapter 1
• Section 4 of chapter 2 is renamed to “Propositions, sets, and the higher truncation levels”
• Section 6 of chapter 2 is split into two, section 6 is named “Propositional truncations” and the new section 7 of chapter 2 is named “Image factorizations”.
• Section 8 of chapter 2 is named “Finite types”
• Section 9 of chapter 2 is named “The univalence axiom”
• Section 10 of chapter 2 is named “Set-quotients”
• Section 11 of chapter 2 is named “Groups in univalent mathematics”

There are no changes to any of the section titles in chapter 3.

• CommentRowNumber28.
• CommentAuthorUrs
• CommentTimeJul 5th 2022

Just out of interest: This is changes with respect to what?

5. The current contents listed on the nLab’s article for this textbook.

6. updated chapters for Egbert’s textbook

Carlo Andolini

• CommentRowNumber31.
• CommentAuthorUrs
• CommentTimeJul 6th 2022
• (edited Jul 6th 2022)

Oh, I see. Thanks, and thanks to Carlo for making the edits (here).

I have gone through it and adjusted/fixed the formatting of the list of book sections a little.

Notice that, for better or worse, our Instiki wiki software here has the “feature” that it generates automatic numberings whenever it senses that the user is typing a numbered list.

On the positive side this means that you can make numbered lists by typing

  1. first point

1. second point

1. third


etc. and be ensured that the numbering always comes out right, even if later somebody adds an item in between the previous first and second point, say.

On the downside it means that if you mean to insist to not start counting at 1, say by typing

  15. this list starts with item 15, because it means to continue a previous list

16. and so its second item wants to be numbered 16

17. and so on


then Instiki will override this decision and start numbering from 1, after all.

To work around this in order to bring out your (Carlo’s) intended list, I have resorted to a little hack and made indented numbered items by typing

  $\;\;\;15.$

$\;\;\;16.$

$\;\;\;17.$


etc. This hack works here (only) because the list items don’t wrap around lines.

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