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I noticed that augmented simplicial set did not point anywhere, so i created the entry. But have no energy to put anything of substance there right now.
I started to put down some details, but I suddenly have to go, so I’ll finish it in a few hours.
I put in the observation that an augmented simplicial set is the same as an ordinary simplicial set with a map to a constant simplicial set. Also, there is an isomorphism of categories $sSet_+ \simeq sSet^\mathbf{2}\times_{sSet} Set$, but I didn’t put this in yet.
I finally filled in my gaps.
regarding degeneracy maps, there isn’t one from $X_{-1}$ to $X_0$, and there only one face map the other way. The sentence about ’for each natural number’ dealing with the case $n=-1$ for face maps is a bit slippery and requires a bit too much negative thinking that early in the article, IMHO. I like the exposition otherwise, and I can’t think how to nicely rewrite it at the moment.
Also we should put in that every simplicial set $X$ is canonically augmented over $\pi_0(X)$.
Done. I actually put in both the left and right adjoints to the underlying unaugmented simplicial set.
I have expanded the entry more.
Moved all that was in the Idea-section to the Definition section and wrote a more genuine Idea-section.
Exapnded in the Definition-section a bit, in particular highlighted the new simplicial identity in degree -1.
Started a section with examples.
Maybe you should add another item to the bug report list
Just to say that, from what Richard kept saying, currently the main version of any page is rendered using his modified rendering engine, while all pages in history etc. use the old engine. That should explain why some effect appears here but not there.
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