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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeJun 22nd 2021

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeJul 10th 2021

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeJul 10th 2021

following:

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeJul 11th 2021
• (edited Aug 28th 2021)

I have expanded (here) the section on examples a tad, making more explicit the form of the non-degenerate simplices in $\Delta[1] \times \Delta[n]$ for general $n$.

In the course of this I have worked a bit on the outline of the entry. I have tried to disentangle general discussion of products of simplicial sets in a first section, from discussion of non-degenerate cells in a second session. I have also turned some really small subsections into numbered remarks, instead. There is still more one could do along these lines, but I’ll leave it as is for now.

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeJul 11th 2021

Added also an example (here) with a tikzcd diagram showing all the non-degenerate simplices in $\Delta[1] \times \Delta[1]$.

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeJul 12th 2021

I have re-written the proposition (here) on the non-degenerate simplices in $\Delta[p] \times \Delta[q]$, now highlighting the transparent characterization as the strictly monotone morphisms of posets

$\Delta[p + q] \longrightarrow \Delta[p] \times \Delta[q] \,.$

This immediately yields the path-notation, for which I added an illustrating tikz-graphics.

• CommentRowNumber7.
• CommentAuthorTim_Porter
• CommentTimeJul 12th 2021

Typo fixed

1. Fixing what I believe is a typo. First time editor.

Kevin Buzzard

• CommentRowNumber9.
• CommentAuthorUrs
• CommentTimeAug 28th 2021

Yes, thanks!!

• CommentRowNumber10.
• CommentAuthorTim_Porter
• CommentTimeAug 28th 2021

There is an image that is not displaying at all. (It seems to have been produced by presheaf.com ….. but I do not see it at all.

(I also removed a } near the non-image.

• CommentRowNumber11.
• CommentAuthorRodMcGuire
• CommentTimeAug 28th 2021
• (edited Aug 28th 2021)

I’m seeing a lot of broken image links from presheaf.com which seems to be down right now.

I can find no notice that Vlad Patryshev has abandoned that site and since he is active on twitter I presume it is only a temporary outage.

https://github.com/vpatryshev/presheaf

All of those images need to be locally rendered, which can be done now.

• CommentRowNumber12.
• CommentAuthorUrs
• CommentTimeAug 28th 2021

Tim, these images are from your original version of the entry, aren’t they?

I did a lot of cleaning up here (or I tried), but I left untouched, for the moment, your material in what is now Section 4 and Section 5, which is where the broken images reside.

• CommentRowNumber13.
• CommentAuthorTim_Porter
• CommentTimeAug 28th 2021
• (edited Aug 28th 2021)

I have not used presheaf.com as far as I can recall. If I have time, I will look back to see when they were added and to try to see what they were intended to be. The problem would seem to be a tikzcddiagram the gives an error message. I do not use tikzcd at present and would not have used it for that diagram. I still use xypic.

I checked back, and the original diagram was done in xypic but using codecogs so someone replaced it.

• CommentRowNumber14.
• CommentAuthorTim_Porter
• CommentTimeAug 30th 2021
• (edited Aug 30th 2021)

I have replaced the faulty diagram with one produced on xypic. (The old one was I think a copy of the one that was given above it.) I am not sure how to alter the spacing which is a bit too expansive.

BTW the editing process is calling presheaf.com and seems unable to connect or to terminate.

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