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

]]>added publication data for:

- {#Friedman08} Greg Friedman,
*An elementary illustrated introduction to simplicial sets*, Rocky Mountain J. Math. 42(2): 353-423 (2012) (arXiv:0809.4221, doi:10.1216/RMJ-2012-42-2-353)

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

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

]]>Added several references.

]]>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). ]]>

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:

The floating table of contents since the last edit had been coded as

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

instead of

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

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

Fixed now!

]]>nLab

simplicial set

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Yes I like it!

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

]]>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.

]]>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.

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

]]>I added the references

Emily Riehl,

*A leisurely introduction to simplicial sets*, 2008, 14 pages (pdf).Pierre Gabriel, Michel Zisman, Calculus of fractions and homotopy theory.

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.

]]>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.)

]]>