Kerodon

Typos: '...in two important respects.' Maybe aspects? only only

Thanks!

A complaint on the comment system: when you write a comment, the commented text disappears, and you have to move back and forth between the two pages. Pretty annoying.

The singular simplicial set $\mathrm{Sing}_{\cdot}(X)$ is a natural candidate for the sort of invariant requested in Question 1.0.0.1: ...

Condition $(∗′)$ requires the existence of an extension only only in the case $0<i<n$, but demands that the extension is unique.

I'm not sure this is the appropriate place for this comment, but I cannot find any general comment section. I'm enjoying and learning a lot with this project and I wonder if there is some (prospective) table of contents for the whole project. If not, what is the expected scope? Is it expected to cover material on higher algebra, derived geometry, spectral algebraic geometry, ...?

We'll see. Baby steps.

There is a typo: "if and only it it". First "it" should be "if".

Yep. Thanks!

This is probably irrelevant: The 'about' page still says claims that kerodon would currently consist of two chapters only. Sorry for commenting here, but I don't think there's an option to comment at the 'about' page.

Good point; we'll fix this with the next update.

This is a question/feature-request regarding the general project: as Kerodon grows, it might be helpful to have a change-log which is more detailed than the major revisions list. Particularly when earlier content is improved resulting in changes to existing material, rather than strict additions. For the stacks project one can see the list of commits (https://stacks.math.columbia.edu/recent-changes) so presumably gerbe supports this, but that might not make sense with Kerodon given that the repo is not public. Even a list of recently modified tags would be a pretty good solution, but I'm not sure if there's a way to do this which doesn't necessitate even more work.

Might I suggest a more ramped intro?

Move this to the first sentence: "∞-categories can be viewed as a simultaneous generalization of homotopy theory and category theory."

And (I believe this is true): "It is a form of algebraic topology, which studies topological spaces by means of algebraic and combinatorial invariants."

"For the following discussion, it assumed that the reader is already familiar with (homotopy theory, category theory, ...?)", ideally with links to internal or external discussions of those subjects.

And then the final paragram and diagram which are currently at the bottom.

In "simple examples", "path components" is noted as a term to be defined (in italics), but not actually defined.

Finally, the instructions for the bot-catcher is kind of confusing. Is "this tag" the "current tag" or do I look somewhere else for it? (Current kind of implies it changes, but 0001 looks hard-coded and unchanging.) What is "the name of the current tag" Is that the four-digit number, or "Comments on Chapter 1", or? I'm going to guess you're looking for 0001; if that's incorrect hopefully there will be some kind of error and it isn't just dropped on the floor.

A grammatical note on the statement of question 1.0.0.2. It says "...What is the relationship between $\operatorname{Sing}_{\bullet }(X)$ with the fundamental groupoid of $X?$" which seems incorrect to me. I believe that replacing the "with" with an "and" here would fix it.

Yep. Thanks!