Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Comments on Section 1.1

Go back to the page of Section 1.1.


Comment #10 by Tim Holzschuh on

In the definition of there is a small typo: , not .

Comment #11 by Kerodon on

Yes, that sounds better. Thanks!

Comment #111 by Emily Pillmore on

Currently the definition of the faces of an n-simplex is the finite collection

.

Shouldn't this be the following?

Sorry for bothering if not! Thanks for all your hard work.

Comment #112 by Emily Pillmore on

Currently the degeneracy maps are defined to be the set of singular -simplices determined by a singular -simplex given by the formula:

.

Shouldn't these degeneracy maps be a map defined thusly?

Thanks, Emily

Comment #113 by Kerodon on

I don't think so; those constructions don't look like they will preserve the property that the coordinates will add up to 1. (Another description of the n-simplex is that it's the set of n-tuples (s_1, ..., s_n) satisfying 0 <= s_1 <= ... <= s_n <= 1; this is related to the description on the page by setting s_i = t_0 + t_1 + ... + t_{i-1}. If you use these new coordinates, then the formula for the face map will look like your proposal for the degeneracy map.)

Comment #114 by Emily Pillmore on

Ah, I see my mistake. Thank you!

Comment #218 by Peng DU on

I'm on the road of a sketch of reading this Kerodon website, and found some small issues in §1.1.

1.I have a small issue about the convention in https://kerodon.net/tag/000Y. I think we'd better not make sense of the symbol Λ^0_0. For if we let Λ^0_0=∅, then consider the Kan fibration ∅→Y for any non-empty Y, it can't have lifting for Λ^0_0=∅→Δ^0 (of course, Λ^0_0=∅→Δ^0 isn't a trivial cofibration, my convention is that all the inclusion of horns Λ^n_i↪Δ^n should be trivial cofibrations).

  1. The diagram in Remark 1.1.5.3 https://kerodon.net/tag/001G, represents a directed graph with three vertices and 5 edges.

3.Before Notation 1.1.8.7, there is the paragraph:"It is possible to deduce Proposition 1.1.8.4 and Corollary 1.1.8.5 in a completely formal way from Lemma 1.1.8.6, since every simplicial set can be presented as a colimit of simplices (see Proposition 1.1.6.18 below)." But Proposition 1.1.6.18 doesn't exist.

4.In proof of Proposition 1.1.8.22 https://kerodon.net/tag/00H5, there is no vertical left arrow in the commutative diagram.

There are also:

  • 11 comment(s) on Chapter 1: The Language of $\infty $-Categories

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 0004. The letter 'O' is never used.