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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeAug 31st 2012

added to simplicial set in the Definition section a slightly more explicit version of the definition.

(I see now this kind of thing is repeated further below in the entry. But it should be right there as a formal definition, I think.)

• CommentRowNumber2.
• CommentAuthorTim_Porter
• CommentTimeAug 31st 2012
That looks good. What do you think should go at the subsection: As models in homotopy theory as we still have a stub there, (even a simple list of the topics might look better?)
• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeAug 31st 2012

What do you think should go at the subsection: As models in homotopy theory as we still have a stub there,

Sorry, I thought it was clear what should go there from the keywords: a brief discussion of how simplicial sets support ordinary homotopy theory as well as directed homotopy theory with pointers to the relevant entries.

• CommentRowNumber4.
• CommentAuthorTim_Porter
• CommentTimeAug 31st 2012
I was merely wondering if you had a more structured entry at this point.
• CommentRowNumber5.
• CommentTimeMay 9th 2013

• Emily Riehl, A leisurely introduction to simplicial sets, 2008, 14 pages (pdf).

• CommentRowNumber6.
• CommentAuthorzskoda
• CommentTimeMay 9th 2013

As Curtis’s article is now free online, I link its doi and MR number to its reference record:

• Edward B. Curtis, Simplicial homotopy theory, Advances in Math. 6 (1971) 107 – 209 MR279808 doi
• CommentRowNumber7.
• CommentAuthorUrs
• CommentTimeJul 24th 2018

added two graphics illustrating simplicial sets here.

I am looking for more and better such graphics. Something one could show on slides to give a good quick idea of what simplicial sets (or at least simplicial complexes) are, without actually giving the definition.

• CommentRowNumber8.
• CommentAuthorTim_Porter
• CommentTimeJul 24th 2018

I made some slight changes to this entry changing the title of one section and adding some brief words on cthe relationship between simplicial complexes and simplicial sets.

• CommentRowNumber9.
• CommentAuthorUrs
• CommentTimeJul 25th 2018

Danny Stevenson has kindly sent me a good illustration of the definition, I have added it here

• CommentRowNumber10.
• CommentAuthorTim_Porter
• CommentTimeJul 25th 2018

Yes I like it!

• CommentRowNumber11.
• CommentAuthorAli Caglayan
• CommentTimeAug 2nd 2018
I can't see anything on the simplicial set page. The history shows that this is definitely the right page. Only the title is showing the rest is compltely empty. Other pages on the nlab load just fine.

nLab
simplicial set
Search
Last revised on July 25, 2018 at 03:47:24. See the history of this page for a list of all contributions to it.

Edit | Back in time (69 revisions) | See changes | History | Cite | Views: Print | TeX | Source
This site is running on Instiki 0.19.7(MML+)
• CommentRowNumber12.
• CommentAuthorUrs
• CommentTimeAug 2nd 2018

Thanks for the alert! I have fixed it now.

This must be because our sysadmin Richard Williamson just recently made some changes to the parsing of pages. The cause of the problem now was this:

  +-- {: .rightHandSide}
+-- {: .toc .clickDown tabindex="0"}
###Context###
#### Homotopy theory
+--{: .hide}
[[!include homotopy - contents]]=--
=--
=--


  +-- {: .rightHandSide}
+-- {: .toc .clickDown tabindex="0"}
###Context###
#### Homotopy theory
+--{: .hide}
[[!include homotopy - contents]]
=--
=--
=--


(as easily happens from copy-and-pasting the ingredients).

Fixed now!

• CommentRowNumber13.
• CommentAuthorAli Caglayan
• CommentTimeAug 2nd 2018
• (edited Aug 2nd 2018)
Interesting problem with the parsing. Perhaps some warnings are needed, detecting edge cases like that, before pages are submitted?

And on another note, the section on directed graphs raises an interesting point. Definitionally, I would of thought that a quiver looks more like a globular set, rather than a simplicial set. Indeed, it seems kind of unnatural to force it to become a simplicial set. Could this be due to similarities of simplicial and globular sets for dimensions less than 2? I have no idea, just an observation.

This isn't the first time I have seen globular sets and directed graphs arise. [I wrote about them in this seperate forum post (by wrote I mean blurted).] (https://nforum.ncatlab.org/discussion/8786/generalising-quiver-representations-to-globular-sets/?Focus=70396#Comment_70396).
• CommentRowNumber14.
• CommentAuthorDmitri Pavlov
• CommentTimeJan 28th 2021

• CommentRowNumber15.
• CommentAuthorDmitri Pavlov
• CommentTimeJan 28th 2021

Added more sources: May, Lamotke, Joyal-Tierney.

• CommentRowNumber16.
• CommentAuthorUrs
• CommentTimeJun 11th 2021

also rearranged the list of references a little, to order them more logically

• CommentRowNumber17.
• CommentAuthorUrs
• CommentTimeJul 13th 2021

Added the statement (here) that every simplicial set is the colimit over its simplices – for completeness.