$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$

Comments on Theorem

Go back to the page of Theorem

Comment #756 by Tim Holzschuh on

Typo in the proof: "From the implication shows that is also locally -cartesian when viewed as an edge of the simplicial set .": maybe "The implication ... shows that... "?

Also shortly before the end of the proof there is a latex line that doesn't get parsed properly (for me at least) right after "together with the following translation of conditions and :".

Comment #760 by Kerodon on

Yep. Thanks!

Comment #1264 by Carles Sáez on

There are some typos in the proof: 1) Along the proof the same map is sometimes called and sometimes . 2) Maps are sometimes called . 3) In condition c), should be . 4) After the first square diagram, "therefore by extended" should be "therefore be extended". 5) In condition , the simplex should be the simplex .

Comment #1697 by Bogdan on

Since is an -category

It should be "since is an -category".

Comment #1699 by Kerodon on

Yep. Thanks!

Comment #2020 by Dennis Chen on

Hey! So I might be missing something, but the induction on the conditions seems to miss the case . I'm thinking of the line "In particular, our inductive hypothesis guarantees that the simplex satisfies condition for ." It seems like this hypothesis assumes the case... is it obviously true or something? Thanks!

Comment #2035 by Kerodon on

When , the assertion that holds for is vacuous.

There are also:

  • 2 comment(s) on Section 5.4: $(\infty ,2)$-Categories
  • 2 comment(s) on Subsection 5.4.4: The Local Thinness Criterion

Post a comment

Your email address will not be published. Required fields are marked.

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).

Unfortunately JavaScript is disabled in your browser, so the comment preview function will not work.

In order to prevent bots from posting comments, we would like you to prove that you are human. You can do this by filling in the name of the current tag in the following input field. As a reminder, this is tag 01X8. The letter 'O' is never used.